Uniqueness of solutions of the stochastic Navier–Stokes equation with invariant measure given by the enstrophy

Abstract

A stochastic Navier–Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure μ_ν whose covariance is given in terms of the enstrophy. Pathwise uniqueness for μ_ν-a.e. initial velocity is proven for solutions having μ_ν as invariant measure.