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Exponential ergodicity for stochastic Burgers and 2D Navier-Stokes equations |
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| Authors: | B. Goldys B. Maslowski |
| Affiliation: | a School of Mathematics, The University of New South Wales, Sydney NSW 2052, Australia b Mathematical Institute, Academy of Sciences of Czech Republic, ?itná 25, 11567 Prague 1, Czech Republic |
| Abstract: | 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. |
| Keywords: | Navier-Stokes equation Burgers equation Additive noise Invariant measure Uniform exponential ergodicity Spectral gap |
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