KUKSIN, Sergei - Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
SHIRIKYAN, Armen - Analyse Numérique et E.D.P., Université Paris-Sud, Bât. 425, 91405 Orsay cedex

Abstract :

We study a complex Ginzburg-Landau (CGL) equation perturbed by a random force which is white in time and smooth in the space variables. Assuming that the space dimension does not exceed four, we prove that this equation has a unique solution and discuss its asymptotic in time properties. Next we consider the case when the random force is proportional to the square root of the viscosity and study the behaviour of stationary solutions as the viscosity goes to zero. We show that, under this limit, a subsequence of solutions in question converges to a nontrivial stationary process formed by global strong solutions of the nonlinear Schrodinger equation.

Article : Fichier Postscript
Contact : Armen.Shirikyan@math.u-psud.fr