The local well-posedness, global existence and ill-posedness for the fifth order Camassa-Holm model
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912648339128320 |
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| author | Chen, Xiaoxin Yin, Zhaoyang |
| author_facet | Chen, Xiaoxin Yin, Zhaoyang |
| contents | In this paper, we consider the fifth order Camassa-Holm model. Firstly, we improve the local well-posedness results in \cite{TangLiu2015,FOCH2021}. Secondly, we give the blow up criteria and conditions for global existence. Finally, when $b=\frac 53$ in the model, we obtain the ill-posedness in $B^1_{\infty,1}$ and $B^{\frac 32}_{2,q}$ with $q\in(1,+\infty]$ in the sense of norm inflation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13165 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The local well-posedness, global existence and ill-posedness for the fifth order Camassa-Holm model Chen, Xiaoxin Yin, Zhaoyang Analysis of PDEs In this paper, we consider the fifth order Camassa-Holm model. Firstly, we improve the local well-posedness results in \cite{TangLiu2015,FOCH2021}. Secondly, we give the blow up criteria and conditions for global existence. Finally, when $b=\frac 53$ in the model, we obtain the ill-posedness in $B^1_{\infty,1}$ and $B^{\frac 32}_{2,q}$ with $q\in(1,+\infty]$ in the sense of norm inflation. |
| title | The local well-posedness, global existence and ill-posedness for the fifth order Camassa-Holm model |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.13165 |