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Volume 10, Number 6, 2020, Pages 2592-2618                                                                DOI:10.11948/20190430
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.
      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 $L^{2}(\mathbf{R}^{3})$. 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 $L^{2}(\mathbf{R}^{3})$ by the tail-estimates of solutions.
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