On nonlinear amplitude evolution under stochastic forcing

The complex Ginzburg-Landau amplitude equation, with or without random forc ing, arises as approximate reductions of complicated physical systems on ex tended spatial domains near bifurcation points. Unlike the deterministic Gi nzburg-Landau equation whose well-posedness is well-known, there seems no r igorous result on global existence and uniqueness of the randomly forced Gi nzburg-Landau equation. Our work provides such a rigorous result on global existence and uniqueness, under very mild conditions. (C) 2000 Elsevier Sci ence Inc. All rights reserved.