Globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913520662085632 |
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| author | Zhou, Yonghui Li, Xiaowan |
| author_facet | Zhou, Yonghui Li, Xiaowan |
| contents | In this paper, we prove that the existence of globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking. We first introduce a new set of independent and dependent variables in connection with smooth solutions, and transform the system into an equivalent semi-linear system. We then establish the global existence of solutions for the semi-linear system via the standard theory of ordinary differential equations. Finally, by the inverse transformation method, we prove the existence of the globally conservative weak solution for the original system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking Zhou, Yonghui Li, Xiaowan Analysis of PDEs Mathematical Physics In this paper, we prove that the existence of globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking. We first introduce a new set of independent and dependent variables in connection with smooth solutions, and transform the system into an equivalent semi-linear system. We then establish the global existence of solutions for the semi-linear system via the standard theory of ordinary differential equations. Finally, by the inverse transformation method, we prove the existence of the globally conservative weak solution for the original system. |
| title | Globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2409.18140 |