KIẾN NGHỊ MỘT SỐ VẤN ĐỀ NGHIÊN CỨU TIẾP THE O

Một phần của tài liệu (LUẬN án TIẾN sĩ) dáng điệu tiệm cận nghiệm của một số lớp phương trình đạo hàm riêng ngẫu nhiên (Trang 124 - 134)

Chương 1 MỘT SỐ KIẾN THỨC CHUẨN BỊ

2. KIẾN NGHỊ MỘT SỐ VẤN ĐỀ NGHIÊN CỨU TIẾP THE O

Bên cạnh các kết quả đã đạt được trong luận án, một số vấn đề mở cần tiếp tục nghiên cứu như:

Tiếp tục nghiên cứu tính chất của tập hút ngẫu nhiên của lớp phương trình parabolic suy biến nhận được trong luận án, chẳng hạn đánh giá số chiều Hausdorff và số chiều fractal, nghiên cứu cấu trúc của tập hút ngẫu nhiên, sự phụ thuộc của tập hút vào tham số trong nhiễu ngẫu nhiên.

Nghiên cứu sự tồn tại và tính ổn định của nghiệm dừng khơng hằng (tức là nghiệm dừng theo nghĩa ngẫu nhiên) của hệ Navier-Stokes-Voigt và hệ Kelvin-Voigt-Brinkmann-Forchheimer ngẫu nhiên.

Nghiên cứu sự hội tụ của nghiệm đối với hệ Navier-Stokes-Voigt ngẫu nhiên khi tham số α dần đến 0, tức là so sánh nghiệm của hệ Navier-

Stokes-Voigt ngẫu nhiên với nghiệm tương ứng của hệ Navier-Stokes ngẫu nhiên.

DANH MỤC CÁC CƠNG TRÌNH KHOA HỌC CỦA TÁC GIẢ LIÊN QUAN ĐẾN LUẬN ÁN

1. C.T. Anh, T.Q. Bao and N.V. Thanh (2012), Regularity of random at- tractors for stochastic semilinear degenerate parabolic equations, Elect. J. Differential Equations, No. 207, 22 pp.

2. C.T. Anh and N.V. Thanh (2016), Asymptotic behavior of the stochastic Kelvin-Voigt-Brinkman-Forchheimer equations, Stoch. Anal. Appl., 34

no. 3, 441-455

3. C.T. Anh and N.V. Thanh (2016), Stabilization of a class of semilinear degenerate parabolic equations by Ito noise, Random Oper. Stoch. Equ.,

24, no. 3, 147-155.

4. C.T. Anh and N.V. Thanh (2018), On the existence and long-time be- havior of solutions to stochastic three-dimensional Navier-Stokes-Voigt equations, Stochastics, 91 (4), 485-513.

5. N.V. Thanh (2018), Internal stabilization of stochastic 3D Navier-Stokes- Voigt equations with linearly multiplicative Gaussian noise, Random Oper. Stoch. Equ., accepted.

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Một phần của tài liệu (LUẬN án TIẾN sĩ) dáng điệu tiệm cận nghiệm của một số lớp phương trình đạo hàm riêng ngẫu nhiên (Trang 124 - 134)