Weak pullback attractors for stochastic Ginzburg-Landau equations in Bochner spaces

Lu Zhang; Aihong Zou; Tao Yan; Ji Shu

doi:10.3934/dcdsb.2021063

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2022, Volume 27, Issue 2: 749-768. Doi: 10.3934/dcdsb.2021063

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Weak pullback attractors for stochastic Ginzburg-Landau equations in Bochner spaces

School of Mathematical Sciences, Laurent Mathematics Center and V.C. & V.R. Key Lab, Sichuan Normal University, Chengdu 610066, China

^* Corresponding author: Ji Shu, shuji@sicnu.edu.cn
^* Corresponding author: Ji Shu, shuji@sicnu.edu.cn

Received: October 2020

Revised: December 2020

Early access: February 24, 2021

Published online: February 24, 2021

The last author is supported by NSFC (11871138).

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Abstract

In this paper we discuss the weak pullback mean random attractors for stochastic Ginzburg-Landau equations defined in Bochner spaces. We prove the existence and uniqueness of weak pullback mean random attractors for the stochastic Ginzburg-Landau equations with nonlinear diffusion terms. We also establish the existence and uniqueness of such attractors for the deterministic Ginzburg-Landau equations with random initial data. In this case, the periodicity of the weak pullback mean random attractors is also proved whenever the external forcing terms are periodic in time.

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Mathematics Subject Classification: Primary: 37L55, 60H15; Secondary: 35Q56.

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