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arXiv · 2608.01863

Exponential mixing for Korteweg-de Vries equation with localized noise

Yuxuan Chen·Shengquan Xiang·Zhifei Zhang·Jia-Cheng Zhao
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Abstract

We establish exponential mixing for the randomly forced and weakly damped KdV equation in $L^2(\mathbb{T})$. 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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Yuxuan Chen, Shengquan Xiang, Zhifei Zhang, Jia-Cheng Zhao. 2026-08-03. Exponential mixing for Korteweg-de Vries equation with localized noise. https://arxiv.org/abs/2608.01863

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