the cpr formulation for the navier stokes equations

... the time-dependent Navier- Stokes equation,” Proceedings of the Japan Academy, vol 36, no 5, pp 273–277, 1960 E B Fabes, B F Jones, and N M Riviere, The initial value problem for the Navier- Stokes ... weak solutions of the Navier- Stokes system,” Journal of Differential Equations, vol 62, no 2, pp 186–212, 1986 M Struwe, “On partial regularity results for the Navier- Stokes equations, ” Communications ... class for the Navier- Stokes equations in Rn ,” Chinese Annals of a Mathematics Series B, vol 16, no 4, pp 407–412, 1995 10 D Chae and J Lee, “Regularity criterion in terms of pressure for the Navier- Stokes...

Ngày tải lên: 22/06/2014, 02:20

... Navier- Stokes/ Brinkman equations An extra (forcing) term in the Navier- Stokes 5.2 Discrete forcing approach 15 equations contains the permeability ( ) of the medium, i.e zero for a solid and infinite for a fluid, ... position of the boundary and the elastic force it exerts on the fluid is then transferred to the cartesian mesh in order to obtain a flow solution To project the forcing on the grid, a smoothed delta ... far is that their performance suffers at higher Reynolds numbers The spreading of the forcing by the smoothed distribution function undermines the local accuracy of the solution in the boundary...

Ngày tải lên: 11/07/2014, 23:20

... NAVIER- STOKES EQUATIONS 1007 Applications to the stochastic 2D Navier- Stokes equations To state the general ergodic result for the two-dimensional Navier- Stokes equations, we begin by looking at the algebraic ... not forbidden and therefore k ∈ Z∞ This shows that Z∞ = Z0 and therefore completes the proof of Proposition 4.4 1011 ERGODICITY OF THE 2D NAVIER- STOKES EQUATIONS 4.2 Malliavin calculus and the ... for the stochastically forced Navier- Stokes equations and other partially dissipative dynamics, Comm Math Phys 230 (2002), 421–462 [Mat03] ——— , On recent progress for the stochastic Navier- Stokes...

Ngày tải lên: 29/03/2014, 07:20

... analytic for ⇠ R2 for ⇠  " Therefore the integrand inside the above integration is correspondingly analytic for ⇠ C2 With Cauchy’s Theorem, we can construct a contour integral to compute Define the ... called the interior wave propagator and the other the surface wave propagator Therefore, it is inevitable to investigate their structures At last, Green’s function of linearized 2-D compressible Navier- Stokes ... structure of the solutions to the compressible Navier- Stokes equations Previous studies that considered the existence and uniqueness of the equations with or without the presence of boundary conditions...

Ngày tải lên: 10/09/2015, 09:06

... them, Liu et al [4] established the local well-posedness of weak solutions to the Navier- Stokes equations; Okada et al [5] obtained the global existence of weak solutions when

Ngày tải lên: 20/06/2014, 22:20

... investigated the Navier- Stokes- Voight equations as an inviscid regularization of the 3D incompressible Navier- Stokes equations, and further obtained the existence of global attractors for Navier- Stokes- Voight ... incompressible Navier- Stokes system which is based on the works of Leray and Hopf Using the weak convergence topology of the space H (see below for the definition), Kapustyan and Valero [7] proved the existence ... Oxford (2004) Hale, JK: Asymptotic Behavior of Dissipative Systems American Mathematical Society, Providence, RI (1988) Hou, Y, Li, K: The uniform attractors for the 2D non-autonomous Navier- Stokes...

Ngày tải lên: 20/06/2014, 21:20

... investigated the Navier- Stokes- Voight equations as an inviscid regularization of the 3D incompressible Navier- Stokes equations, and further obtained the existence of global attractors for Navier- Stokes- Voight ... incompressible Navier- Stokes system which is based on the works of Leray and Hopf Using the weak convergence topology of the space H (see below for the definition), Kapustyan and Valero [7] proved the existence ... Oxford (2004) Hale, JK: Asymptotic Behavior of Dissipative Systems American Mathematical Society, Providence, RI (1988) Hou, Y, Li, K: The uniform attractors for the 2D non-autonomous Navier- Stokes...

Ngày tải lên: 20/06/2014, 22:20

... variables of these equations have different meaning The variables of the Navier- Stokes equations are thermodynamical parameters while the variables of the Boltzmann equations or the Broadwell ... many others They can also be used to study the magnetohydrodynamics if been coupled with Maxwell equations However, the existence and the smoothness of the solutions to the Navier- Stokes equations ... the mathematicians This fact is somehow surprising considering the wide range of practical applications of the equations As a result, the study of the Navier- Stokes equations becomes one of the...

Ngày tải lên: 09/09/2015, 10:15

... of these equations are yet to be explored For some recent work on equations of fractional order with deviated arguments, see [46-48] and the references therein In this article, we consider the ... completed the main part of this paper, SKN and LZ corrected the main theorems and gave two examples All authors read and approved the final manuscript Competing interests The authors declare that they ... mentioning that the conditions of our theorems are easily to verify, so they are applicable to a variety of problems, see Examples 4.1 and 4.2 The proof of our main results is based upon the following...

Ngày tải lên: 21/06/2014, 03:20

... theory, bioscience, physics, etc This class of equations play an important role in modeling phenomena of the real world So it is valuable to discuss the properties of the solutions of these equations ... Difference Equations Proof The approach of the proof is very similar to those in 17, 19, 20 Here, we omit it Theorem 3.2 Provided that conditions (H1 )–(H4 ) hold, then the system 2.2 with the conditions ... integral inequality Theorem 4.1 Supposed that the conditions of Theorem 3.2 holds, then the solution of the system 2.2 with conditions 2.3 and 2.4 is exponential stable in mean square if the inequality...

Ngày tải lên: 21/06/2014, 11:20

... finish the proof of the main result, Theorem 1.9 Just as , we will use the following two lemmas The first lemma is the following integral inequality Lemma 3.1 see Let φ ∈ Δ2 ∩ ∇2 , g ∈ Lφ Rn Then for ... estimates for the general linear higher-order parabolic equations with the help of fundamental solutions and Green functions Moreover, in 11 we proved global Schauder estimates for the initial-value ... using the uniform approach as the second-order case Recently we generalized the local Lp estimates to the Orlicz space φ D2m u Q1/6 φ |ut |2 dz ≤ C dz Q1/6 φ f φ |u|2 dz dz Q1/2 1.6 Q1/2 for ut...

Ngày tải lên: 21/06/2014, 16:20

... > for large k are negative see 19 , that is, > wk > wk Then using the same argument as in the first part of the proof we have < vk < vk for large k for any solution v of 5.15 , that is, u is the ... 22−p for p ∈ 1, Denote t q − 1/ p − , then we need to prove the inequality g t : t − · 2−1/t ≥ for t ∈ 1, ∞ A standard investigation of the graph of the function t → · 2−1/t shows that the required ... it is called the minimal solution of 2.1 If w is the distinguished solution of 2.1 , then the associated solution of 1.1 given by the formula k−1 Φ−1 xk j m wj rj is said to be the recessive...

Ngày tải lên: 21/06/2014, 20:20

... trace bounds for the product of two general matrices The new trace bounds improve the previous results Then, we present some trace bounds for the solution of the algebraic Riccati equations, which ... that our bounds for the trace are the tightest among the parallel trace bounds in symmetric case Then, we have obtained some trace bounds for the solution of the algebraic Riccati equations, which ... proposed for the trace of matrix products 2, 6–8, 17–20 , and 18 is the tightest among the parallel results In 1995, Lasserre showed 18 the following given any matrix A ∈ Rn×n , B ∈ Sn , then the...

Ngày tải lên: 22/06/2014, 03:20

... + Vn−1 Vn Qn )1/2 By the Hadamard theorem on homeomorphism, (3.1) has a unique solution Pn xn+1 and Qn−1 xn for all n This completes the proof of Theorem 3.3 In the next theorem, without loss ... index IDEs is the fact that the pencil {A(t),B(t)} in the continuous case is always of index for all t ∈ J, while for n 1, {An ,Bn } is not necessarily of index Now, we describe shortly the decomposition ... operator connecting two subspaces Nn−1 ,Nn In the remainder of this paper, for the sake of simplicity, the norm of Rm is assumed to be Euclidean Theorem 3.3 Let (3.1) be of index Moreover, suppose...

Ngày tải lên: 23/06/2014, 00:20

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Ngày tải lên: 27/03/2015, 15:54

... [10] for a survey) for uniformly elliptic equation with L p right hand side Remark 1.2 By the Localization Theorem [6, 7], we have Bcθ1/2 /|logθ| ∩ Ω ⊂ S θ ⊂ BCθ1/2 |logθ| ∩ Ω Therefore, Theorem ... 2,q (Ω) where q > p, then Theorem 1.3 is a consequence of the global W 2,p estimates for solutions to the linearized Monge-Amp`ere equations [4, Theorem 2] In this case, the proof in [4] is quite ... 1.3, the condition p > n is sharp, since even in the uniformly elliptic case (for example, when φ(x) = 12 |x|2 , Lφ is the Laplacian), the global C 1,α estimates fail when p = n We prove Theorem...

Ngày tải lên: 16/10/2015, 09:28