The local well-posedness, blow-up phenomena and ill-posedness of a new fifth-order Camassa-Holm type equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911211054956544 |
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| author | Lian, Yiyao Yin, Zhaoyang |
| author_facet | Lian, Yiyao Yin, Zhaoyang |
| contents | In this paper, we study a new fifth-order Camassa-Holm type equation derived by Li \cite{Li.Z}. We firstly establish the local well-posedness in the sense of Hadamard for the Cauchy problem of the new fifth-order Camassa-Holm type equation in Besov spaces. Secondly, we obtain blow-up criteria. Building upon this, by utilizing the conservation laws and establishing local boundedness, we derive a blow-up result that precisely determines the blow-up time. Finally, the ill-posedness of the new fifth-order Camassa-Holm type equation in the critical Sobolev space $H^{\frac{1}{2}}$ is established via a norm inflation argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The local well-posedness, blow-up phenomena and ill-posedness of a new fifth-order Camassa-Holm type equation Lian, Yiyao Yin, Zhaoyang Analysis of PDEs In this paper, we study a new fifth-order Camassa-Holm type equation derived by Li \cite{Li.Z}. We firstly establish the local well-posedness in the sense of Hadamard for the Cauchy problem of the new fifth-order Camassa-Holm type equation in Besov spaces. Secondly, we obtain blow-up criteria. Building upon this, by utilizing the conservation laws and establishing local boundedness, we derive a blow-up result that precisely determines the blow-up time. Finally, the ill-posedness of the new fifth-order Camassa-Holm type equation in the critical Sobolev space $H^{\frac{1}{2}}$ is established via a norm inflation argument. |
| title | The local well-posedness, blow-up phenomena and ill-posedness of a new fifth-order Camassa-Holm type equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.13164 |