# American Institute of Mathematical Sciences

October  2019, 24(10): 5621-5632. doi: 10.3934/dcdsb.2019075

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

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

* Corresponding author: Jianhua Huang

Received  October 2018 Published  April 2019

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

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.

Citation: Yan Zheng, Jianhua Huang. Exponential convergence for the 3D stochastic cubic Ginzburg-Landau equation with degenerate noise. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5621-5632. doi: 10.3934/dcdsb.2019075
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