The asymptotic behavior of solutions to three-dimensional Navier-Stokes equations with nonlinear damping

被引：51

作者：

Jia, Yan ^{[1
]}

Zhang, Xingwei ^{[1
]}

Dong, Bo-Qing ^{[1
]}

机构：

[1] Anhui Univ, Sch Math Sci, Hefei 230039, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2011年 / 12卷 / 03期

关键词：

Navier-Stokes equations; Nonlinear damping; L(2) decay; Higher-order derivative; Asymptotic stability; LARGE TIME BEHAVIOR; HIGHER-ORDER DERIVATIVES; WEAK SOLUTIONS; L2; DECAY; STABILITY; FLOWS; MODEL; R-2; RN;

D O I：

10.1016/j.nonrwa.2010.11.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper concerns the asymptotic behavior of solutions to three-dimensional Navier-Stokes equations with nonlinear damping |u|(beta-1)u. We first study the L(2) decay of weak solutions with beta >= 10/3 by developing the classic Fourier splitting method. Second, for 7/2 <= beta < 5, we prove the optimal upper bounds of the higher-order derivative of the strong solution by employing a new analysis technique. Finally, we investigate the asymptotic stability of the large solution to the system with beta >= 7/2 under large initial perturbation. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1736 / 1747

页数：12

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