Pullback dynamics of 3D Navier-Stokes equations with nonlinear viscosity

被引：11

作者：

Yang, Xin-Guang ^{[1
]}

Feng, Baowei ^{[2
]}

Wang, Shubin ^{[3
]}

Lu, Yongjin ^{[4
]}

Ma, To Fu ^{[5
]}

机构：

[1] Henan Normal Univ, Dept Math & Informat Sci, Xinxiang 453007, Peoples R China

[2] Southwestern Univ Finance & Econ, Coll Econ Math, Chengdu 611130, Sichuan, Peoples R China

[3] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

[4] Virginia State Univ, Dept Math & Econ, Petersburg, VA 23806 USA

[5] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP, Brazil

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2019年 / 48卷

基金：

巴西圣保罗研究基金会; 美国国家科学基金会;

关键词：

Navier-Stokes equations; Nonlinear viscosity; Pullback attractors; Fractal dimension; Ladyzhenskaya model; UPPER SEMICONTINUITY; ATTRACTORS; DIMENSION; EXISTENCE;

D O I：

10.1016/j.nonrwa.2019.01.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with pullback dynamics of 3D Navier-Stokes equations with variable viscosity and subject to time-dependent external forces. Our main result establishes the existence of finite-dimensional pullback attractors in a general setting involving tempered universes. We also present a sufficient condition on the viscosity coefficients that guarantees the attractors are nontrivial. We end the paper by showing the upper semi-continuity of pullback attractors as the non-autonomous perturbation vanishes. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：337 / 361

页数：25

共 41 条

[1]

[Anonymous], 1933, J. Math. Pures Appl.

[2]

Boyer F., 2013, APPL MATH SCI, V183

[3] Upper semicontinuity of attractors for small random perturbations of dynamical systems [J].

Caraballo, T ;

Langa, JA ;

Robinson, JC .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1998, 23 (9-10) :1557-1581

[4] Pullback attractors for asymptotically compact non-autonomous dynamical systems [J].

Caraballo, T ;

Lukaszewicz, G ;

Real, J .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (03) :484-498

[5]

Carvalho A. N., 2013, APPL MATH SCI, V182

[6] The long-time dynamics of 3D non-autonomous Navier-Stokes equations with variable viscosity [J].

Chen, Yongqiang ;

Yang, Xin-Guang ;

Si, Mengmeng .

SCIENCEASIA, 2018, 44 (01) :18-26

[7]

Chepyzhov VV, 2004, DISCRETE CONT DYN-A, V10, P117

[8]

Chepyzhov VV, 2001, ATTRACTORS EQUATIONS

[9] GLOBAL LYAPUNOV EXPONENTS, KAPLAN-YORKE FORMULAS AND THE DIMENSION OF THE ATTRACTORS FOR 2D NAVIER-STOKES EQUATIONS [J].

CONSTANTIN, P ;

FOIAS, C .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (01) :1-27

[10] ON THE DIMENSION OF THE ATTRACTORS IN TWO-DIMENSIONAL TURBULENCE [J].

CONSTANTIN, P ;

FOIAS, C ;

TEMAM, R .

PHYSICA D, 1988, 30 (03) :284-296

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