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arXiv · 2509.01921

Ergodicity for the randomly forced Korteweg-de Vries-Burgers equation

Peng Gao
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Abstract

Our goal in this paper is to investigate ergodicity of the randomly forced Korteweg-de Vries-Burgers(KdVB) equation driven by non-additive white noise. Under reasonable conditions, we show that exponential ergodicity for KdVB equation driven by a space-time localised noise and ergodicity for KdVB equation driven by a multiplicative white noise. Our proof is based on some newly developed analytical properties for KdVB equation, such as Carleman estimate, truncated observability inequality, Foia\c{s}-Prodi estimate. Combining these analytical properties with coupling method and asymptotic coupling method, we can investigate the long time behavior of randomly forced KdVB equation.

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Peng Gao. 2025-09-02. Ergodicity for the randomly forced Korteweg-de Vries-Burgers equation. https://arxiv.org/abs/2509.01921

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