SMS scnews item created by Daniel Daners at Tue 2 Sep 2014 1648
Type: Seminar
Modified: Wed 3 Sep 2014 0910
Distribution: World
Expiry: 8 Sep 2014
Calendar1: 8 Sep 2014 1400-1500
CalLoc1: AGR Carslaw 829

PDE Seminar

Quasipotential and exit time for 2D Stochastic Navier-Stokes equations driven by space time white noise


Zdzisław Brzeźniak
University of York, UK
8 Sep 2014, 2-3pm, Carslaw Room 829 (AGR)


We are dealing with the Navier-Stokes equation in a bounded regular domain D of 2, perturbed by an additive Gaussian noise wδt, that 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 S0,T δ and the corresponding quasi-potential Uδ and, by using arguments from relaxation and Γ-convergence we show that Uδ converges to a limiting quasi-potential 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 U0 is explicitly computed.

Finally, we apply these results to estimate 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.

This talk is based on a joint work with Sandra Cerrai and Mark Freidlin.

Check also the PDE Seminar page. Enquiries to Daniel Hauer or Daniel Daners.

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