On the convergence of the two-dimensional second grade fluid model to the Navier-Stokes equation

被引：5

作者：

Arada, Nadir ^{[1
,2
]}

机构：

[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicacoes, P-2829516 Quinta Da Torre, Caparica, Portugal

[2] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, P-2829516 Quinta Da Torre, Caparica, Portugal

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 03期

关键词：

Second grade fluids; Navier-Stokes equations; Navier-slip boundary conditions; Uniform a priori estimates; Rate of convergence; BOUNDARY-CONDITIONS; EULER EQUATIONS; CLASSICAL-SOLUTIONS; COMPLEX FLUID; ALPHA; LIMIT; TURBULENCE; EXISTENCE;

D O I：

10.1016/j.jde.2015.10.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the equations governing the motion of incompressible second grade fluids in a bounded two-dimensional domain with Navier-slip boundary conditions. We first prove that the corresponding solutions are uniformly bounded with respect to the normal stress modulus alpha in the L-infinity-H-1 and the L-2-H-2 time-space norms. Next, we study their asymptotic behavior when alpha tends to zero, prove that they converge to regular solutions of the Navier-Stokes equations and give the rate of convergence in terms of alpha. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：2557 / 2586

页数：30

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