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arXiv · 2308.13865

Non-uniform convergence of solution for the Camassa-Holm equation in the zero-filter limit

Jinlu Li·Yanghai Yu·Weipeng Zhu
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Abstract

In the short note, we prove that given initial data $\mathcal{u}_0 \in \pmb{H}^s(\mathbb{R})$ with $s>\frac32$ and for some $T>0$, the solution of the Camassa-Holm equation does not converges uniformly with respect to the initial data in $\pmb{L}^\infty$ $(0,T;H^s(\mathbb{R}))$ to the inviscid Burgers equation as the filter parameter $\alpha$ tends to zero. This is a supplement to our recent result on the zero-filter limit.

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Jinlu Li, Yanghai Yu, Weipeng Zhu. 2023-08-26. Non-uniform convergence of solution for the Camassa-Holm equation in the zero-filter limit. https://arxiv.org/abs/2308.13865

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