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March  2021, 26(3): 1615-1626. doi: 10.3934/dcdsb.2020175

## Ergodicity of stochastic damped Ostrovsky equation driven by white noise

 1 College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China 2 College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

* Corresponding author: Jianhua Huang

Received  December 2019 Revised  February 2020 Published  May 2020

Fund Project: The authors are supported by the NSF of China(No.11771449)

The current paper is devoted to the stochastic damped Ostrovsky equation driven by white noise. By establishing the uniform estimates for the solution in $H^1$ norm, we prove the global well-posedness and the existence of invariant measure for stochastic damped Ostrovsky equation with random initial value. Moreover, we obtain the ergodicity of stochastic damped Ostrovsky equation with deterministic initial conditions.

Citation: Shang Wu, Pengfei Xu, Jianhua Huang, Wei Yan. Ergodicity of stochastic damped Ostrovsky equation driven by white noise. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1615-1626. doi: 10.3934/dcdsb.2020175
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