AN A POSTERIORI CONDITION ON THE NUMERICAL APPROXIMATIONS OF THE NAVIER-STOKES EQUATIONS FOR THE EXISTENCE OF A STRONG SOLUTION

被引:8
作者
Dashti, Masoumeh [1 ]
Robinson, James C. [1 ]
机构
[1] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England
关键词
Navier-Stokes equations; regularity of solutions; rigorous numerics;
D O I
10.1137/060677537
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In their 2006 paper, Chernyshenko et al. [J. Math. Phys., 48 (2007), 065204, 15 pp]. prove that a sufficiently smooth strong solution of the 3D Navier-Stokes equations is robust with respect to small enough changes in initial conditions and forcing function. They also show that if a regular enough strong solution exists, then Galerkin approximations converge to it. They then use these results to conclude that the existence of a sufficiently regular strong solution can be verified using sufficiently refined numerical computations. In this paper we study the strong solutions with less regularity than those considered in Chernyshenko et al. [J. Math. Phys., 48 (2007), 065204, 15 pp]. We prove a similar robustness result and show the validity of the results relating convergent numerical computations and the existence of the strong solutions.
引用
收藏
页码:3136 / 3150
页数:15
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