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arXiv · 2010.08747

Non-uniform dependence for the two-component Camassa-Holm shallow water system

Jinlu Li·Yanghai Yu·Weipeng Zhu
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Abstract

In this paper, we consider the solution map of the initial value problem to the two-component Camassa-Holm equation on the line. We prove that the solution map of this problem is not uniformly continuous in Sobolev spaces $H^s(\R)\times H^{s-1}(\R)$ for $s>3/2$.

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Jinlu Li, Yanghai Yu, Weipeng Zhu. 2020-10-17. Non-uniform dependence for the two-component Camassa-Holm shallow water system. https://arxiv.org/abs/2010.08747

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