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Random attractors for non-autonomous fractional stochastic Ginzburg-Landau equations on unbounded domains
Ji Shu,Jian Zhang
Keywords:Non-autonomous stochastic fractional Ginzburg-Landau equation; Random dynamical system; Random attractor; Additive noise; Upper semicontinuity
Abstract:
      This paper deals with the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg-Landau equations driven by additive noise with $\alpha\in(0,1)$. The main difficulty is the noncompactness of Sobolev embeddings on unbounded domains, so we establish the pullback asymptotic compactness of solutions in $L^{2}(\mathbf{R}^{3})$ by the tail-estimates of solutions. Consequently, we prove the existence and uniqueness of tempered pullback random attractors for the equations in $L^{2}(\mathbf{R}^{3})$. At last, we obtain the upper semicontinuity of random attractors when the intensity of noise approaches zero.