On nonlinear amplitude evolution under stochastic forcing

摘要

The complex Ginzburg–Landau amplitude equation, with or without random forcing, arises as approximate reductions of complicated physical systems on extended spatial domains near bifurcation points. Unlike the deterministic Ginzburg–Landau equation whose well-posedness is well-known, there seems no rigorous result on global existence and uniqueness of the randomly forced Ginzburg–Landau equation. Our work provides such a rigorous result on global existence and uniqueness, under very mild conditions.