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arXiv · 2104.05973

Ill-posedness for the Camassa-Holm and related equations in Besov spaces

Jinlu Li·Yanghai Yu·Weipeng Zhu
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Abstract

In this paper, we give a construction of $u_0\in B^\sigma_{p,\infty}$ such that corresponding solution to the Camassa-Holm equation starting from $u_0$ is discontinuous at $t = 0$ in the metric of $B^\sigma_{p,\infty}$, which implies the ill-posedness for this equation in $B^\sigma_{p,\infty}$. We also apply our method to the b-equation and Novikov equation.

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Jinlu Li, Yanghai Yu, Weipeng Zhu. 2021-04-13. Ill-posedness for the Camassa-Holm and related equations in Besov spaces. https://arxiv.org/abs/2104.05973

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