Blowup analysis of a Camassa-Holm type equation with time-varying dissipation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914426968342528 |
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| author | Zhou, Yonghui Li, Xiaowan Ji, Shuguan |
| author_facet | Zhou, Yonghui Li, Xiaowan Ji, Shuguan |
| contents | This paper is concerned with the local well-posedness, wave breaking, blow-up rate for a Camassa-Holm type equation with time-dependent weak dissipation. Firstly, we obtain the local well-posedness of solutions by using Kato's theory. Secondly, by using energy estimates, characteristic methods, and comparison principles, we derive two blowup criteria involving both pointwise gradient conditions and mixed amplitude-gradient conditions, and prove the blowup rate is universally $-2$. Our results extend wave breaking analysis to physically relevant variable dissipation regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26534 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Blowup analysis of a Camassa-Holm type equation with time-varying dissipation Zhou, Yonghui Li, Xiaowan Ji, Shuguan Analysis of PDEs Mathematical Physics This paper is concerned with the local well-posedness, wave breaking, blow-up rate for a Camassa-Holm type equation with time-dependent weak dissipation. Firstly, we obtain the local well-posedness of solutions by using Kato's theory. Secondly, by using energy estimates, characteristic methods, and comparison principles, we derive two blowup criteria involving both pointwise gradient conditions and mixed amplitude-gradient conditions, and prove the blowup rate is universally $-2$. Our results extend wave breaking analysis to physically relevant variable dissipation regimes. |
| title | Blowup analysis of a Camassa-Holm type equation with time-varying dissipation |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2603.26534 |