Global existence and blow-up for the Euler-Poincaré equations with a class of initial data
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911863209459712 |
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| author | Li, Jinlu Yu, Yanghai Zhu, Weipeng |
| author_facet | Li, Jinlu Yu, Yanghai Zhu, Weipeng |
| contents | In this paper we investigate the Cauchy problem of d-dimensional Euler-Poincaré equations. By choosing a class of new and special initial data, we can transform this d-dimensional Euler-Poincaré equations into the Camassa-Holm type equation in the real line. We first obtain some global existence results and then present a new blow-up result to the system under some different assumptions on this special class of initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01252 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence and blow-up for the Euler-Poincaré equations with a class of initial data Li, Jinlu Yu, Yanghai Zhu, Weipeng Analysis of PDEs In this paper we investigate the Cauchy problem of d-dimensional Euler-Poincaré equations. By choosing a class of new and special initial data, we can transform this d-dimensional Euler-Poincaré equations into the Camassa-Holm type equation in the real line. We first obtain some global existence results and then present a new blow-up result to the system under some different assumptions on this special class of initial data. |
| title | Global existence and blow-up for the Euler-Poincaré equations with a class of initial data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.01252 |