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

摘要: We are dealing with the Navier-Stokes equation in a bounded regular domain $$\mathcal {O}$$ of $$\mathbb {R}^2$$ , perturbed by an additive Gaussian noise $$\partial w^{Q_\delta }/\partial t$$ which is white time and colored space. assume that correlation radius gets smaller as $$\delta \searrow 0$$ so converges to space time. For every >0$$ we introduce large deviation action functional $$S^\delta _{T}$$ corresponding quasi-potential $$U_\delta $$ and, using arguments from relaxation $$\Gamma -convergence show $$U=U_0$$ spite fact has no meaning square integrable functions, when space-time noise. Moreover, case periodic boundary conditions limiting $$U$$ explicitly computed. Finally, apply these results estimate asymptotics expected exit solution stochastic basin attraction asymptotically stable point for unperturbed system.