Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noise

In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main challenge is to establish time asymptotic smoothing properties of...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 269; no. 4; pp. 3686 - 3720
Main Authors Peng, Xuhui, Huang, Jianhua, Zhang, Rangrang
Format Journal Article
LanguageEnglish
Published Elsevier Inc 05.08.2020
Subjects
Ergodic
Exponential mixing
Malliavin calculus
Real Ginzburg-Landau equation
60H07
Malliavin calculus
Ergodic
60H15
Real Ginzburg-Landau equation
Exponential mixing
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Summary:In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system. To achieve this, we propose a condition which only requires four noises.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2020.03.013