B. Goldys, B. Maslowski
EXPONENTIAL ERGODICITY FOR STOCHASTIC BURGERS AND 2D NAVIER-STOKES EQUATIONS
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ABSTRACT.  It is shown that transition measures of the stochastic 
Navier-Stokes equation in dimension 2 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 trasformation. Analogous results are proved for the stochastic Burgers equation.