Polynomial mixing for white-forced Kuramoto-Sivashinsky equation on the whole line
Dynamical Systems
2024-11-19 v2 Analysis of PDEs
Probability
Abstract
Our goal in this paper is to investigate ergodicity of white-forced Kuramoto-Sivashinsky equation (KSE) on the whole line. Under the assumption that sufficiently many directions of the phase space are stochastically forced, we can prove that the dynamics is attractive toward a unique invariant probability measure with polynomial rate of any power. In order to prove this, we further develop coupling method and establish a sufficiently general criterion for polynomial mixing. The proof of polynomial mixing for KSE is obtained by the combination of the coupling criterion and the Foia\c{s}-Prodi estimate of KSE on the whole line.
Keywords
Cite
@article{arxiv.2408.00592,
title = {Polynomial mixing for white-forced Kuramoto-Sivashinsky equation on the whole line},
author = {Peng Gao},
journal= {arXiv preprint arXiv:2408.00592},
year = {2024}
}