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

We are dealing with the Navier-Stokes equation in a bounded regular domain of , perturbed by an additive Gaussian noise , which 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 , 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 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.