Exponential mixing for Korteweg-de Vries equation with localized noise
Yuxuan Chen, Shengquan Xiang, Zhifei Zhang, Jia-Cheng Zhao
Abstract
We establish exponential mixing for the randomly forced and weakly damped KdV equation in L2(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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