Ill-posedness for the higher dimensional Camassa-Holm equations in Besov spaces

Min Li; Yingying Guo

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arXiv · 2106.00540

Ill-posedness for the higher dimensional Camassa-Holm equations in Besov spaces

Min Li·Yingying Guo

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Abstract

In the paper, by constructing a initial data $u_{0}\in B^{\sigma}_{p,\infty}$ with $\sigma-2>\max\{1+\frac 1 p, \frac 3 2\}$, we prove that the corresponding solution to the higher dimensional Camassa-Holm equations starting from $u_{0}$ is discontinuous at $t=0$ in the norm of $B^{\sigma}_{p,\infty}$, which implies that the ill-posedness for the higher dimensional Camassa-Holm equations in $B^{\sigma}_{p,\infty}$.

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Min Li, Yingying Guo. 2021-06-01. Ill-posedness for the higher dimensional Camassa-Holm equations in Besov spaces. https://arxiv.org/abs/2106.00540

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