Random Attractors for Stochastic Ginzburg-Landau Equation on Unbounded Domains

Abstract

We prove the existence of a pullback attractor in L2(ℝn) for the stochastic Ginzburg-Landau equation with additive noise on the entire n-dimensional space ℝn. We show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. We demonstrate that the system possesses a unique D-random attractor, for which the asymptotic compactness is established by the method of uniform estimates on the tails of its solutions.