Blow-Up Theory and Liouville-Type Theorem for Solutions of a Class of Generalized Camassa-Holm-Kadomtsev-Petviashvili Equations
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908854241984512 |
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| author | Ke, Xueli Wang, Jiamin Zang, Aibin |
| author_facet | Ke, Xueli Wang, Jiamin Zang, Aibin |
| contents | We investigate the blow-up behavior and Liouville-type theorems of solutions to a class of generalized Camassa-Holm-Kadomtsev-Petviashvili (CH-KP) equations with a generally smooth nonlinear term $g(u)$. First, using the continuation method, we establish a blow-up criterion that is independent of the regularity index of initial data. Under the assumption that $ g'(u)$ is uniformly bounded, we prove the blow-up theorem and a weighted blow-up result by means of characteristic lines, a priori estimates and the Riccati inequality. Moreover, we extend these blow-up results to the setting where $g'(u)$ is polynomially controlled, which includes typical nonlinearities such as $ g(u)=κu+3u^2 $ for the classical CH-KP equations. Furthermore, a Liouville-type uniqueness theorem is established under the condition $g(u) \geq γu^2$ with $u \neq 0$, $g(u)>γu^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22933 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Blow-Up Theory and Liouville-Type Theorem for Solutions of a Class of Generalized Camassa-Holm-Kadomtsev-Petviashvili Equations Ke, Xueli Wang, Jiamin Zang, Aibin Analysis of PDEs We investigate the blow-up behavior and Liouville-type theorems of solutions to a class of generalized Camassa-Holm-Kadomtsev-Petviashvili (CH-KP) equations with a generally smooth nonlinear term $g(u)$. First, using the continuation method, we establish a blow-up criterion that is independent of the regularity index of initial data. Under the assumption that $ g'(u)$ is uniformly bounded, we prove the blow-up theorem and a weighted blow-up result by means of characteristic lines, a priori estimates and the Riccati inequality. Moreover, we extend these blow-up results to the setting where $g'(u)$ is polynomially controlled, which includes typical nonlinearities such as $ g(u)=κu+3u^2 $ for the classical CH-KP equations. Furthermore, a Liouville-type uniqueness theorem is established under the condition $g(u) \geq γu^2$ with $u \neq 0$, $g(u)>γu^2$. |
| title | Blow-Up Theory and Liouville-Type Theorem for Solutions of a Class of Generalized Camassa-Holm-Kadomtsev-Petviashvili Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.22933 |