Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

被引：0

作者：

Ren, Junbai ^{[1
]}

机构：

[1] Jiangxi Univ Finance & Econ, Res Ctr Appl Stat, Sch Stat, Nanchang 330013, Peoples R China

来源：

ABSTRACT AND APPLIED ANALYSIS | 2014年

关键词：

V-ATTRACTORS; L2; DECAY;

D O I：

10.1155/2014/879780

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with L-p - L-q estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C-1(1 + t)(-3/4) <= parallel to u parallel to(L2) (1 + t)(-3/4), t > 1. The decay rate is optimal since it coincides with that of heat equation.

引用

页数：5

共 14 条

[1] PARTIAL REGULARITY OF SUITABLE WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS [J].

CAFFARELLI, L ;

KOHN, R ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1982, 35 (06) :771-831

[2]

Caraballo T, 2008, DISCRETE CONT DYN-B, V10, P760

[3]

Caraballo T, 2006, ADV NONLINEAR STUD, V6, P411

[4] Asymptotic Behavior of Solutions to Liquid Crystal Systems in R3 [J].

Dai, Mimi ;

Qing, Jie ;

Schonbek, Maria .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2012, 37 (12) :2138-2164

[5] On the weak strong uniqueness of Koch Tataru's solution for the Navier-Stokes equations [J].

Dong, Bo-Qing ;

Zhang, Zhifei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (07) :2406-2422

[6] 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

[7] Asymptotic profile of solutions to the two-dimensional dissipative quasi-geostrophic equation [J].

Dong BoQing ;

Liu QingQing .

SCIENCE CHINA-MATHEMATICS, 2010, 53 (10) :2733-2748

[8] The asymptotic behavior of solutions to three-dimensional Navier-Stokes equations with nonlinear damping [J].

Jia, Yan ;

Zhang, Xingwei ;

Dong, Bo-Qing .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (03) :1736-1747

[9] ON L2 DECAY OF WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS IN RN [J].

KAJIKIYA, R ;

MIYAKAWA, T .

MATHEMATISCHE ZEITSCHRIFT, 1986, 192 (01) :135-148

[10] Pullback V-attractors of the 3-dimensional globally modified Navier-Stokes equations [J].

Kloeden, Peter E. ;

Langa, Jose A. ;

Real, Jose .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2007, 6 (04) :937-955

← 1 2 →