Existence and uniqueness of the global conservative solutions for the generalized Camassa-Holm equation with dual-power nonlinearities
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912964841308160 |
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| author | Chen, Xiaoxin Chen, Jian Yin, Zhaoyang |
| author_facet | Chen, Xiaoxin Chen, Jian Yin, Zhaoyang |
| contents | In this paper, we investigate the global conservative solutions to the generalized Camassa-Holm equation with dual-power nonlinearities. By introducing a new set of variables, we transform the original equation into an equivalent semi-linear system, which allows us to establish the global existence of conservative solutions. Furthermore, for a given global conservative solution, we construct some auxiliary variables tailored to its specific structure and demonstrate that they satisfy a semi-linear system with a unique solution, thereby deriving the uniqueness of conservative solutions to the original equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12978 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of the global conservative solutions for the generalized Camassa-Holm equation with dual-power nonlinearities Chen, Xiaoxin Chen, Jian Yin, Zhaoyang Analysis of PDEs In this paper, we investigate the global conservative solutions to the generalized Camassa-Holm equation with dual-power nonlinearities. By introducing a new set of variables, we transform the original equation into an equivalent semi-linear system, which allows us to establish the global existence of conservative solutions. Furthermore, for a given global conservative solution, we construct some auxiliary variables tailored to its specific structure and demonstrate that they satisfy a semi-linear system with a unique solution, thereby deriving the uniqueness of conservative solutions to the original equation. |
| title | Existence and uniqueness of the global conservative solutions for the generalized Camassa-Holm equation with dual-power nonlinearities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.12978 |