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ĐẠI HỌC THÁI NGUYÊN TRƯỜNG ĐẠI HỌC SƯ PHẠM 33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PMTieu
Trang 1ĐẠI HỌC THÁI NGUYÊN
TRƯỜNG ĐẠI HỌC SƯ PHẠM
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 2ĐẠI HỌC THÁI NGUYÊN
TRƯỜNG ĐẠI HỌC SƯ PHẠM
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 3LỜI CẢM ƠN
Luận văn này được hoàn thành dưới sự hướng dẫn của TS.Phạm Thị Thủy Do đây là những kiến thức khá mới mẻ và khoảng thời gian nghiên cứu còn hạn chế nên luận văn không tránh khỏi những sai sót.Tôi rất mong nhận được những ý kiến đóng góp của quý thầy cô và mọi người để luận
văn được hoàn thiện hơn
Tôi cũng xin bày tỏ lòng biết ơn sâu sắc tới TS Phạm Thị Thủy đã trực tiếp giao đề tài, hướng dẫn và giúp đỡ tận tình trong suốt quá trình nghiên cứu và hoàn thành luận văn Tôi xin chân thành cảm ơn Ban chủ nhiệm Khoa Toán cùng các quý thầy cô đã quan tâm, nhiệt tình giảng dạy trong suốt khóa học Tôi cũng xin cảm ơn gia đình, bạn bè đã giúp đỡ tôi trong suốt quá trình học và
hoàn thành luận văn Trân trọng cảm ơn!
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 4LỜI CAM ĐOAN
Tôi xin cam đoan rằng nội dung trình bày trong luận văn này là trung thực và không trùng lặp với đề tài khác Tôi cũng xin cam đoan rằng mọi sự giúp đỡ cho việc thực hiện luận văn này đã được cảm ơn và các thông tin trích dẫn trong luận văn đã được chỉ rõ nguồn gốc
Thái Nguyên, tháng 7 năm 2021
Người viết luận văn
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 5MỤC LỤC
123docz.net - File bi loi xin lienhe: lethikim34079@hotmail.com Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 6Lời nói đầu
Hệ phương trình Navier-Stokes lần đầu tiên được nghiên cứu vào năm 1822 Từ đó đến nay, đã có nhiều công trình nghiên cứu về hệ phương trình này Muốn hiểu được hiện tượngchuyển động của dòng chảy chất lỏng và không khí tự nhiên, sóng dập sau đuôi con tàu chạy trên mặt nước, hiện tượng hỗn loạn của không khí sau đuôi máybay khi bay trên bầu trời chúng ta đều phải tìm cách giải phương trình Navier – Stokes Do đó, việc nghiên cứu sự tồn tại nghiệm, tính duy nhất nghiệm, tính chính quy của nghiệm, đẳng thức năng lượng và đánh giá của nghiệm là rất cần thiết Việc nghiên cứu các tính chất định tính của nghiệm, chẳng hạn tính chính quy của nghiệm của các phương trình vi phân đóng vai trò cực kỳ quan trọng trong lý thuyết phương trình đạo hàm riêng Gần đây có nhiều tác giả quan tâm nghiên cứu về hệ phương trình Navier-Stokes và đã đạt được những thành tựu quan trọng như T Buckmaster, Z Liang, A Giorgini, A Miranville, J Shuai, R Temam,…Đặc biệt, phương pháp sử dụng đẳng thức năng lượng để nghiên cứu tính chính quy của nghiệm được nhiều nhà khoa học quan tâm
Luận văn: “Tiêu chuẩn chính quy cho hệ phương trình Navier-Stokes nén được” nghiên cứu và trình bày sự tồn tại, tính chính quy của nghiệm của hệ phương trình Cahn-Hilliard-Navier-Stokesnén được, mối quan hệ giữa bảo toàn năng lượng và bậc chính quy cho nghiệm yếu
Cahn-Hilliard-Luận văn được bố cục thành 2 chương cùng với lời nói đầu, kết luận và danh mục tài liệu tham khảo Trong đó, Chương 2 là nội dung chính của luận văn
Chương 1: Kiến thức chuẩn bị
Chương này trình bày các khái niệm và kết quả cơ sở cần thiết được sử dụng trong Chương 2
Chương 2: Tính chính quy dựa trên đẳng thức năng lượng cho hệ phương trình
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 7Chương 1
Kiến thức chuẩn bị
Trong chương này, chúng tôi trình bày về phương trình Navier-Stokes; một số các không gian hàm và tính chất, các bất đẳng thức thông dụng và một vài khái niệm khác để bổ trợ cho việc nghiên cứu Chương 2 Tài liệu được trích dẫn từ [1],[3],[7],[10]
1.1 Phương trình Navier-Stokes
Giả sử n là miền tổng quát, không rỗng với biên là
Cho u t x( ), =(u t x u t x1( ) ( ), , 2 , , ,u t xn( ), )là vận tốc của chất lỏng tại điểm
( ) (t x, = t x x, ,12, ,xn),t[0, ),Tx và cho p t x( ), là áp suất của chất lỏng tại
uv uuupfu
− + + =
(1.1) với t0,T),x, hệ phương trình này được gọi là hệ phương trình Navier-
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Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 8Hơn nữa, ta sẽ thêm điều kiện ban đầu u( )0=u0 (1.3)với vận tốc ban đầu u0tại thời điểm t =0 Điều này có nghĩa là
( )0, 0( ),
Hệ phương trình (1.1) cùng với điều kiện (1.2), (1.3) được gọi là bài toán với điều kiện hỗn hợp ban đầu f u, 0 cho hệ phương trình Navier-Stokes Trong (1.1) bỏ qua số hạng phi tuyến u.uta được hệ phương trình Navier-Stokes tuyến tính và
0, (0) ,
gọi là hệ Stokes không dừng
0.
v upfdiv uu
Bỏ qua uttrong (1.1) ta được hệ Navier-Stokes dừng
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
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33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 91.2 Các không gian hàm 1.2.1 Không gian hàm trơn
Cho kN, thì C k( ) là không gian của tất cả các hàmu: → ,xu x( )
thỏa mãn D u tồn tại và liên tục trong với 0n, 0 k 0( )
C là không gian các hàm liên tục u →:
được gọi là không gian của các hàm trơn trên
Kí hiệu M là bao đóng của tập M Thì
Suppu = x u x được gọi là giá trị của hàm u →:
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 101.2.2 Không gian qL
Định nghĩa Cho n,n1, là một miền, và cho 1 q thì L q( )được định nghĩa là không gian Banach của các hàm đo được Lebesgue u xác định trên
cùng với chuẩn hữu hạn
cùng với chuẩn ess-sup hữu hạn
, L () L : ess-sup ( )
xu = u = u = u = u x
Đặt ' :1
1.2.3 Không gian Sobolev
Lý thuyết của phương trình Navier-Stokes sẽ được xác định bằng cách sử dụng các không gian Sobolev bên dưới Ở đây nlà một miền tùy ý với n 1 Giả sử kNvà 1 q thì không gian q
L - Sobolev bậc ,
Wk q( )
k được định nghĩa là không gian của mọi uLq( ) sao cho
( )
D u L với mọi k,Chuẩn trong ,
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 11( )
( ) CkGF C
không đổi với mọiC0( ).
Không gian tuyến tính C0( ) ' của tất cả các phiếm hàm tuyến tính
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 12Đặc biệt, với mỗi 1
( )
f L , hàm suy rộng D f =D f ,.C0( ) 'được định nghĩa bởi
kDa D
( )
f L và ( 1, , ) n0n
= Nếu D f chính quy, 1
( )
D f L ta gọi D f đạo hàm cấp cao yếu hoặc đạo hàm suy rộng của f Nếu 1 q , kí hiệu
( ),
qD f L
tức là D f chính quy và là một hàm chứa trong L q( ) Ta viết đơn giản ( )
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 13
= nghĩa là Df chính quy và là một hàm trong L q( )
Ta cần các không gian tương ứng cho trường vectơ Giả sử mNvà
F, = F, := F1,1+ Fm,m.Ta gọi
= Thì f =( , ,f1 fm)định nghĩa hàm suy rộng
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 14Kí hiệu D F Df D F , , và Df được định nghĩa như trên Ví dụ, giả sử
( )n
uL với u, : u, , C0,( ), ta được phép nhúng tự nhiên
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 15( ) ( ) '.
L C Sau đó, ta sẽ sử dụng phép chiếu trực giao
: ( )n ( )
P L →L từ 2
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM332412067:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
Trang 16f p c
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM33Wednesday, June 12, 20247:57:25 PM7:57:25 PM
Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocTieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duoc
33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM33Wednesday, June 12, 20247:57:26 PM7:57:26 PM
33Tieu chuan chinh quy cho he phuong trinh Cahn Hilliard Navier Stokes nen duocWednesday, June 12, 2024
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