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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Brzezniak, Z.¹  Caraballo, T.²  Langa, J. A.²  Li, Y.³  Lukaszewicz, G.⁴  Real, J.² 

[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

关键词: Random attractors;    Energy method;    Asymptotically compact random dynamical systems;    Stochastic Navier-Stokes;    Unbounded domains;   

DOI  :  10.1016/j.jde.2013.07.043

来源: Elsevier

【 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.

【 授权许可】

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