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

被引：48

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

共 26 条

[1] Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model [J].

Bresch, D ;

Desjardins, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 238 (1-2) :211-223

[2] Weak and strong solutions for the incompressible Navier-Stokes equations with damping [J].

Cai, Xiaojing ;

Jiu, Quansen .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 343 (02) :799-809

[3]

Chen Z., 1997, ADV MATH SCI APPL, V7, P741

[4] A SHARP DECAY RESULT ON STRONG SOLUTIONS OF THE NAVIER-STOKES EQUATIONS IN THE WHOLE SPACE [J].

CHEN, ZM .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1991, 16 (4-5) :801-820

[5] Time decay rates of the isotropic non-Newtonian flows in Rn [J].

Dong, Bo-Qing .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2007, 23 (01) :99-106

[6] Remarks on upper and lower bounds of solutions to the Navier-Stokes equations in R2 [J].

Dong, Bo-Qing ;

Chen, Zhi-Min .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 182 (01) :553-558

[7] On the decay of higher order derivatives of solutions to Ladyzhenskaya model for incompressible viscous flows [J].

Dong BoQing ;

Jiang Wei .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (05) :925-934

[8] Large time behavior to the system of incompressible non-Newtonian fluids in R2 [J].

Dong, BQ ;

Li, YS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 298 (02) :667-676

[9] On the decay properties of solutions to the non-stationary Navier-Stokes equations in R3 [J].

He, C ;

Xin, ZP .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2001, 131 :597-619

[10]

Hsiao L., 1997, QUASILINEAR HYPERBOL

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