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Ergodicity for a class of Markov processes and applications to randomly forced PDE'S. II

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  • The paper is devoted to studying the problem of ergodicity for the complex Ginzburg--Landau (CGL) equation perturbed by an external random force. We show that the conditions of a simple general result established in [22] are fulfilled for the equation in question. As a consequence, we prove that the corresponding family of Markov processes has a unique stationary distribution, which possesses a mixing property. The result of this paper was announced in the joint work with Sergei Kuksin [14].
    Mathematics Subject Classification: Primary: 35K55, 60J25; Secondary: 35Q60, 60H15.


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