Ergodicity of stochastic damped Ostrovsky equation driven by white noise

Shang Wu; Pengfei Xu; Jianhua Huang; Wei Yan

doi:10.3934/dcdsb.2020175

Article Contents

2021, Volume 26, Issue 3: 1615-1626. Doi: 10.3934/dcdsb.2020175

This issue Previous Article On a terminal value problem for a system of parabolic equations with nonlinear-nonlocal diffusion terms Next Article Ground state homoclinic orbits for a class of asymptotically periodic second-order Hamiltonian systems

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
^* Corresponding author: Jianhua Huang

Received: November 30, 2019

Revised: January 31, 2020

Early access: May 2020

Published: March 2021

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

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Abstract

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.

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

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