Exponential convergence for the 3D stochastic cubic Ginzburg-Landau equation with degenerate noise

Yan Zheng; Jianhua Huang

doi:10.3934/dcdsb.2019075

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2019, Volume 24, Issue 10: 5621-5632. Doi: 10.3934/dcdsb.2019075

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Exponential convergence for the 3D stochastic cubic Ginzburg-Landau equation with degenerate noise

Yan Zheng and
Jianhua Huang^,

College of Science, National University of Defense Technology, Changsha 410073, China

^* Corresponding author: Jianhua Huang
^* Corresponding author: Jianhua Huang

Received: October 2018

Early access: April 2019

Published: August 2019

The authors are supported by the NSF of China(No.11771449), NSF of Hunan(No.2018JJ2468), Fundamental Program of NUDT(No.ZK17-03-19).

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Abstract

The current paper is devoted to 3D stochastic Ginzburg-Landau equation with degenerate random forcing. We prove that the corresponding Markov semigroup possesses an exponentially attracting invariant measure. To accomplish this, firstly we establish a type of gradient inequality, which is also essential to proving asymptotic strong Feller property. Then we prove that the corresponding dynamical system possesses a strong type of Lyapunov structure and is of a relatively weak form of irreducibility.

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Mathematics Subject Classification: Primary: 60H15; Secondary: 37A25.

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References

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