Exponential ergodicity for stochastic Burgers and 2D Navier-Stokes equations

It is shown that transition measures of the stochastic Navier-Stokes equation in 2D converge exponentially fast to the corresponding invariant measures in the distance of total variation. As a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state transformation. Analogous results are proved for the stochastic Burgers equation.