Ill-posedness for the Cauchy problem of the modified Camassa-Holm equation in $B^0_{\infty,1}$

Zhen He; Zhaoyang Yin

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arXiv · 2310.15749

Ill-posedness for the Cauchy problem of the modified Camassa-Holm equation in $B^0_{\infty,1}$

Zhen He·Zhaoyang Yin

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Abstract

In this paper, we prove the norm inflation and get the ill-posedness for the modified Camassa-Holm equation in $B_{\infty,1}^0$. Therefore we completed all well-posedness and ill-posedness problem for the modified Camassa-Holm equation in all critical spaces $B_{p,1}^\frac{1}{p}$ with $p\in[1,\infty]$.

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Zhen He, Zhaoyang Yin. 2023-10-24. Ill-posedness for the Cauchy problem of the modified Camassa-Holm equation in $B^0_{\infty,1}$. https://arxiv.org/abs/2310.15749

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