Convergence of transport noise to Ornstein-Uhlenbeck for 2D Euler equations under the enstrophy measure

Abstract

We consider the vorticity form of the 2D Euler equations which is perturbed by a suitable transport type noise and has white noise initial condition. It is shown that, under certain conditions, this equation converges to the 2D Navier-Stokes equation driven by the space-time white noise.