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

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Publication details

JournalTransactions of the American Mathematical Society
DatePublished - 24 Jul 2006
Issue number12
Number of pages42
Pages (from-to)5587-5629
Original languageEnglish


We introduce a notion of an asymptotically compact (AC) random dynamical system (RDS).We prove that for an AC RDS the O-limit set OB(¿) 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.

    Research areas

  • stochastic Navier-Stokes equations, unbounded domains, cylindrical white noise, asymptotic compactness, random dynamic systems, absorbing sets, DIFFERENTIAL-EQUATIONS, EVOLUTION-EQUATIONS, INVARIANT-MEASURES, GLOBAL ATTRACTOR, DRIVEN, REGULARITY, DIMENSION, EXISTENCE, SYSTEMS, NOISE

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