Nowhere-uniform continuity of the solution map of the Camassa-Holm equation in Besov spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910334300717056 |
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| author | Li, Jinlu Yu, Yanghai Zhu, Weipeng |
| author_facet | Li, Jinlu Yu, Yanghai Zhu, Weipeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_08190 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nowhere-uniform continuity of the solution map of the Camassa-Holm equation in Besov spaces Li, Jinlu Yu, Yanghai Zhu, Weipeng Analysis of PDEs 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. |
| title | Nowhere-uniform continuity of the solution map of the Camassa-Holm equation in Besov spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2207.08190 |