RANDOM ATTRACTORS FOR NON-AUTONOMOUS FRACTIONAL STOCHASTIC GINZBURG-LANDAU EQUATIONS ON UNBOUNDED DOMAINS

Abstract

This paper deals with the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg-Landau equations driven by additive noise with $ \alpha\in(0,1) $. We prove the existence and uniqueness of tempered pullback random attractors for the equations in $ L^{2}({\bf{R}}^{3}) $. In addition, we also obtain the upper semicontinuity of random attractors when the intensity of noise approaches zero. The main difficulty here is the noncompactness of Sobolev embeddings on unbounded domains. To solve this, we establish the pullback asymptotic compactness of solutions in $ L^{2}({\bf{R}}^{3}) $ by the tail-estimates of solutions.