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

Xuhui Peng; Jianhua Huang; Rangrang Zhang

doi:10.1016/j.jde.2020.03.013

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

Xuhui Peng
, Jianhua Huang
, Rangrang Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Hunan Normal University
National University of Defense Technology

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	3686-3720
Number of pages	35
Journal	Journal of Differential Equations
Volume	269
Issue number	4
DOIs	https://doi.org/10.1016/j.jde.2020.03.013
Publication status	Published - 5 Aug 2020

Keywords

Ergodic
Exponential mixing
Malliavin calculus
Real Ginzburg-Landau equation

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10.1016/j.jde.2020.03.013

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abstract = "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.",

keywords = "Ergodic, Exponential mixing, Malliavin calculus, Real Ginzburg-Landau equation",

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AU - Peng, Xuhui

AU - Huang, Jianhua

AU - Zhang, Rangrang

PY - 2020/8/5

Y1 - 2020/8/5

N2 - 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.

AB - 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.

KW - Ergodic

KW - Exponential mixing

KW - Malliavin calculus

KW - Real Ginzburg-Landau equation

UR - https://www.scopus.com/pages/publications/85081212673

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M3 - Article

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SN - 0022-0396

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EP - 3720

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -

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

Abstract

Keywords

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