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
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.
|Institution:||The University of York|
|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|
|Publisher:||American Mathematical Society|