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

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