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   \mu_{\nu} whose covariance is given in terms of the enstrophy. Pathwise uniqueness for \mu_{\nu}-a.e. initial velocity is proven for solutions having \mu_{\nu} as invariant measure. 
S. Albeverio and B. Ferrario