Ergodicity for the stochastic Complex Ginzburg-Landau equations
  We study a stochastic complex Ginzburg--Landau (CGL) equation driven by a smooth noise in space and we establish exponential convergence of the Markovian transition semi-group toward a unique invariant probability measure. Since Doob Theorem does not seem not to be useful in our situation, a coupling method is used. In order to make this method easier to understand, we first focus on two simple examples which contain most of the arguments and the essential difficulties. 
Cyril Odasso (IRMAR)