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. © 2005 Elsevier Inc. All rights reserved.