Polynomial mixing for white-forced Kuramoto-Sivashinsky equation on the whole line

2024/08/01 by Gao, Peng · 1 citation
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2408.00592

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 Foiaş-Prodi estimate of KSE on the whole line.

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• Exponential mixing for the stochastic Kuramoto-Sivashinsky equation on the 1D torus

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