Research output: Contribution to journal › Article

Journal | Transactions of the American Mathematical Society |
---|---|

Date | Published - 24 Jul 2006 |

Issue number | 12 |

Volume | 358 |

Number of pages | 42 |

Pages (from-to) | 5587-5629 |

Original language | English |

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.

- 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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