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

Ji Shu; Jian Zhang

doi:10.11948/20190430

2020 Volume 10 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2020 > 10(6): 2592-2618

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Ji Shu, Jian Zhang. RANDOM ATTRACTORS FOR NON-AUTONOMOUS FRACTIONAL STOCHASTIC GINZBURG-LANDAU EQUATIONS ON UNBOUNDED DOMAINS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2592-2618. doi: 10.11948/20190430

Citation:

Ji Shu, Jian Zhang. RANDOM ATTRACTORS FOR NON-AUTONOMOUS FRACTIONAL STOCHASTIC GINZBURG-LANDAU EQUATIONS ON UNBOUNDED DOMAINS[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2592-2618. doi: 10.11948/20190430

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

Ji Shu^1,,
Jian Zhang^2, ,

1.
School of Mathematical Sciences and V.C. & V.R. Key Lab, Sichuan Normal University, Chengdu 610068, China
2.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Author Bio: Email: shuji@sicnu.edu.cn(J. Shu)
Corresponding author: Email: zhangjiancdv@sina.com(J. Zhang)
Fund Project: The authors were supported by National Natural Science Foundation of China (No.11871138), joint research project of Laurent Mathematics Center of Sichuan Normal University and National-Local Joint Engineering Laboratory of System Credibility Automatic Verification

Abstract

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.
- Non-autonomous stochastic fractional Ginzburg-Landau equation /
- random dynamical system /
- random attractor /
- additive noise /
- upper semicontinuity
MSC: 37L55, 60H15, 35Q56

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