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arXiv · 2207.08190

Nowhere-uniform continuity of the solution map of the Camassa-Holm equation in Besov spaces

Jinlu Li·Yanghai Yu·Weipeng Zhu
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Abstract

In the paper, we gave a strengthening of our previous work in [32] (J. Differ. Equ. 269 (2020)) and proved that the data-to-solution map for the Camassa-Holm equation is nowhere uniformly continuous in $B^s_{p,r}(\R)$ with $s>\max\{1+1/{p},3/2\}$ and $(p,r)\in [1,\infty]\times[1,\infty)$. The method applies also to the b-family of equations which contain the Camassa-Holm and Degasperis-Procesi equations.

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Jinlu Li, Yanghai Yu, Weipeng Zhu. 2022-07-17. Nowhere-uniform continuity of the solution map of the Camassa-Holm equation in Besov spaces. https://doi.org/10.1007/s00332-022-09866-x

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