Ergodicity for the stochastic complex Ginzburg--Landau equations (Q2507600)

The paper deals with the stochastic complex Ginzburg-Landau equation driven by a smooth noise in space. The aim of the paper is to study ergodicity for this equation under very general assumptions. The method used in this paper is a combination of two main ideas: a coupling method in a sufficiently general framework and the Foias-Prodi estimates. The author proves exponential convergence of the Markov transition semigroup toward a unique invariant probability measure. Two simple examples are discussed in the paper, which highlight the most important arguments in the method.