Ground state homoclinic orbits for a class of asymptotically periodic second-order Hamiltonian systems
On a terminal value problem for a system of parabolic equations with nonlinear-nonlocal diffusion terms
March 2021, 26(3): 1615-1626. doi: 10.3934/dcdsb.2020175
Ergodicity of stochastic damped Ostrovsky equation driven by white noise
Shang Wu 1, , Pengfei Xu 1, , Jianhua Huang 1,, and Wei Yan 2,
College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China
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.
Keywords: Invariant measure, damped Ostrovsky equation, white noises.
Mathematics Subject Classification: Primary: 60H15; Secondary: 37A25.
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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Shang Wu Pengfei Xu Jianhua Huang Wei Yan