Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

被引：57

作者：

Brzezniak, Z. ^{[1
]}

Caraballo, T. ^{[2
]}

Langa, J. A. ^{[2
]}

Li, Y. ^{[3
]}

Lukaszewicz, G. ^{[4
]}

Real, J. ^{[2
]}

机构：

[1] Univ York, Dept Math, York Y010 5DD, N Yorkshire, England

[2] Univ Seville, Dpto Ecuac Diferenciales & Anal Numer, E-41080 Seville, Spain

[3] Huazhong Univ Sci & Technol, Informat Engn & Simulat Ctr, Wuhan 430074, Peoples R China

[4] Univ Warsaw, Inst Appl Math & Mech, PL-02097 Warsaw, Poland

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 255卷 / 11期

基金：

英国工程与自然科学研究理事会; 中国国家自然科学基金;

关键词：

Random attractors; Energy method; Asymptotically compact random dynamical systems; Stochastic Navier-Stokes; Unbounded domains; PULLBACK ATTRACTORS; GLOBAL ATTRACTOR; STOKES EQUATIONS; EXISTENCE; FLOW;

D O I：

10.1016/j.jde.2013.07.043

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a Poincare-like domain has a unique random attractor. One of the technical problems associated with the rough noise is overcomed by the use of the corresponding Cameron-Martin (or reproducing kernel Hilbert) space. Our results complement the result by Brzezniak and Li (2006) [10] who showed that the corresponding flow is asymptotically compact and also generalize Caraballo et al. (2006) [12] who proved existence of a unique attractor for the time-dependent deterministic Navier-Stokes equations. (C) 2013 Published by Elsevier Inc.

引用

页码：3897 / 3919

页数：23

共 37 条

[1] EXISTENCE AND FINITE DIMENSIONALITY OF THE GLOBAL ATTRACTOR FOR EVOLUTION-EQUATIONS ON UNBOUNDED-DOMAINS [J].