Research output: Contribution to journal › Article › peer-review

Journal | Probability Theory and Related Fields |
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Date | E-pub ahead of print - 18 Nov 2014 |

Date | Published (current) - Aug 2015 |

Volume | 162 |

Number of pages | 55 |

Pages (from-to) | 739–793 |

Early online date | 18/11/14 |

Original language | English |

We are dealing with the Navier-Stokes equation in a bounded regular domain O of R2, perturbed by an additive Gaussian noise ∂wQδ/∂t, which is white in time and colored in space. We assume that the correlation radius of the noise gets smaller and smaller as δ↘0, so that the noise converges to the white noise in space and time. For every δ>0 we introduce the large deviation action functional SδT and the corresponding quasi-potential Uδ and, by using arguments from relaxation and Γ-convergence we show that Uδ converges to U=U0, in spite of the fact that the Navier-Stokes equation has no meaning in the space of square integrable functions, when perturbed by space-time white noise. Moreover, in the case of periodic boundary conditions the limiting functional U is explicitly computed. Finally, we apply these results to estimate of the asymptotics of the expected exit time of the solution of the stochastic Navier-Stokes equation from a basin of attraction of an asymptotically stable point for the unperturbed system.

- 60H15, 60F10, 35Q30, 49J45

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