Ill-posedness for the periodic Camassa--Holm type equations in the end-point critical Besov space $B^{1}_{\infty,1}$

Jinlu Li; Yanghai Yu; Weipeng Zhu

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arXiv · 2303.05671

Ill-posedness for the periodic Camassa--Holm type equations in the end-point critical Besov space $B^{1}_{\infty,1}$

Jinlu Li·Yanghai Yu·Weipeng Zhu

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Abstract

For the real-line case, it is shown that both the Camassa--Holm \cite{Guo} and Novikov equations \cite{Li-arx} are ill-posed in $B_{\infty,1}^{1}$. In this paper, by presenting a new construction of initial data which leads to the norm inflation phenomena, we prove that both the periodic Camassa--Holm and Novikov equations are also ill-posed in $B_{\infty,1}^{1}$.

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Jinlu Li, Yanghai Yu, Weipeng Zhu. 2023-03-10. Ill-posedness for the periodic Camassa--Holm type equations in the end-point critical Besov space $B^{1}_{\infty,1}$. https://arxiv.org/abs/2303.05671

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