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 of , perturbed by an additive Gaussian noise , that is white in time and colored in space. We assume that the correlation radius of the noise gets smaller and smaller as , so that the noise converges to the white noise in space and time. For every we introduce the large deviation action functional and the corresponding quasi-potential and, by using arguments from relaxation and -convergence we show that converges to a limiting quasi-potential , 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 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.