Large deviation for Navier-Stokes equations with small stochastic perturbation

Abstract

We consider a Navier-Stokes evolution equation with a small stochastic perturbation. The unperturbed Navier-Stokes equation approximates incompressible, viscous fluid flows in a two-dimensional bounded region with an adhesive boundary condition. The small stochastic perturbation accounts for often ignored quantum effects and other sources of fluctuations. The weak solution process for the stochastic Navier-Stokes equation is constructed via a Girsanov-type transformation. Large deviation results in terms of Wentzel-Freidlin estimates are obtained for both the infinite-dimensional Brownian motion and the weak solution process for the stochastic Navier-Stokes equation.