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arXiv · 2204.14151

Ill-posedness for the two component Degasperis-Procesi equation in critical Besov space

Jinlu Li·Min Li·Weipeng Zhu
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Abstract

In this paper, we study the Cauchy problem for the two component Degasperis-Procesi equation in critical Besov space $B^1_{\infty,1}(\mathbb R)$. By presenting a new construction of initial data, we proved the norm inflation of the corresponding solutions in $B^1_{\infty,1}(\mathbb R)$ and hence ill-posedness. This is quite different from the local well-posedness result for the Degasperis-Procesi equation in critical Besov space $B^1_{\infty,1}(\mathbb R)$ due to the coupled structure of density function.

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Jinlu Li, Min Li, Weipeng Zhu. 2022-04-29. Ill-posedness for the two component Degasperis-Procesi equation in critical Besov space. https://arxiv.org/abs/2204.14151

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