Exponential mixing for Korteweg-de Vries equation with localized noise

2026/08/03 by Yuxuan Chen, Shengquan Xiang, Zhifei Zhang +1
Mathematics · #math.AP #math.DS #math.OC #math.PR #msc:35Q53 #msc:35R60 #msc:37A25 #msc:93C20

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arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

We establish exponential mixing for the randomly forced and weakly damped KdV equation in L²(\mathbbT). The noise is bounded, localized, and degenerate in high frequencies. Our proof relies on a general probabilistic framework in [11,33], nonlinear smoothing for KdV and its linearization via normal form transformation, and stabilization of the system by localized force. This paper continues a series of works connecting asymptotic compactness, control theory, and ergodicity and mixing for randomly forced dispersive PDEs.

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