PULLBACK EXPONENTIAL ATTRACTORS FOR THE THREE DIMENSIONAL NON-AUTONOMOUS NAVIER-STOKES EQUATIONS WITH NONLINEAR DAMPING

被引：10

作者：

Li, Fang ^{[1
]}

You, Bo ^{[2
]}

机构：

[1] Xidian Univ, Sch Math & Stat, Xian 710126, Shaanxi, Peoples R China

[2] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 01期

基金：

美国国家科学基金会;

关键词：

Navier-Stokes equations; nonlinear damping; pullback exponential attractor; the methods of l-trajectories; LARGE TIME BEHAVIOR; GLOBAL ATTRACTORS; WEAK SOLUTIONS; CONVERGENCE; REGULARITY; UNIQUENESS;

D O I：

10.3934/dcdsb.2019172

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main objective of this paper is to study the long-time behavior of solutions for the three dimensional non-autonomous Navier-Stokes equations with nonlinear damping for r > 4: Inspired by the the methods of l-trajectories in [27], we will prove the existence of a finite dimensional pullback attractor and a pullback exponential attractor, which gives another way of considering the long-time behavior of the non-autonomous evolutionary equations.

引用

页码：55 / 80

页数：26

共 41 条

[1] Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations [J].

Ball, JM .

JOURNAL OF NONLINEAR SCIENCE, 1997, 7 (05) :475-502

[2] 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

[3] On some compressible fluid models: Korteweg, lubrication, and shallow water systems [J].

Bresch, D ;

Desjardins, B ;

Lin, CK .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2003, 28 (3-4) :843-868

[4] 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

[5] PULLBACK EXPONENTIAL ATTRACTORS FOR EVOLUTION PROCESSES IN BANACH SPACES: THEORETICAL RESULTS [J].

Carvalho, Alexandre N. ;

Sonner, Stefanie .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (06) :3047-3071

[6]

Chepyzhov VV., 2002, Attractors for Equations of Mathematical Physics

[7] On global attractors of the 3D Navier-Stokes equations [J].

Cheskidov, A. ;

Foias, C. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 231 (02) :714-754

[8] Uniform global attractors for the nonautonomous 3D Navier Stokes equations [J].

Cheskidov, Alexey ;

Lu, Songsong .

ADVANCES IN MATHEMATICS, 2014, 267 :277-306

[9] Pullback exponential attractors for nonautonomous equations Part I: Semi linear parabolic problems [J].

Czaja, Radoslaw ;

Efendiev, Messoud .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (02) :748-765

[10] Stability behaviors of Leray weak solutions to the three-dimensional Navier-Stokes equations [J].

Dong, Bo-Qing ;

Jia, Yan .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2016, 30 :41-58

← 1 2 3 4 5 →