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

Abstract It is shown that transition measures of the stochastic Navier–Stokes equation in 2 D 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.

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