Asymptotic behavior for non-autonomous fractional stochastic Ginzburg–Landau equations on unbounded domains

Abstract

In this paper, we first prove the existence and uniqueness of tempered pullback random attractors for a non-autonomous stochastic fractional Ginzburg–Landau equation driven by multiplicative noise with α ∈ (0, 1) in L2R3. Then, we obtain the upper semicontinuity of random attractors when the intensity of noise approaches zero. Due to the lack of the compactness of Sobolev embeddings on unbounded domains, we establish the pullback asymptotic compactness of solutions in L2(R3) by the tail-estimates of solutions.