White Rose University Consortium logo
University of Leeds logo University of Sheffield logo York University logo

Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains

Brzezniak, Z. and Yuhong, L. (2006) Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains. Transactions of the American Mathematical Society, 358 (12). pp. 5587-5629. ISSN 1088-6850

Full text not available from this repository.

Abstract

We introduce a notion of an asymptotically compact (AC) random dynamical system (RDS).We prove that for an AC RDS the Ω-limit set ΩB(ω) of any bounded set B is nonempty, compact, strictly invariant and attracts the set B. We establish that the 2D Navier Stokes Equations (NSEs) in a domain satisfying the Poincar´e inequality perturbed by an additive irregular noise generate an AC RDS in the energy space H. As a consequence we deduce existence of an invariant measure for such NSEs. Our study generalizes on the one hand the earlier results by Flandoli-Crauel (1994) and Schmalfuss (1992) obtained in the case of bounded domains and regular noise, and on the other hand the results by Rosa (1998) for the deterministic NSEs.

Item Type: Article
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 14 May 2009 15:07
Last Modified: 17 May 2009 16:07
Published Version: http://dx.doi.org/1090/S0002-9947-06-03923-7
Status: Published
Publisher: American Mathematical Society
Refereed: Yes
Identification Number: 10.1090/S0002-9947-06-03923-7
URI: http://eprints.whiterose.ac.uk/id/eprint/7706

Actions (login required)

View Item View Item