Well-posedness and no-uniform dependence for the Euler-Poincaré equations in Triebel-Lizorkin spaces
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909142415835136 |
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| author | Zhong, Yuanhua Lu, Jianzhong Li, Min Li, Jinlu |
| author_facet | Zhong, Yuanhua Lu, Jianzhong Li, Min Li, Jinlu |
| contents | In this paper, we study the Cauchy problem of the Euler-Poincaré equations in $\R^d$ with initial data belonging to the Triebel-Lizorkin spaces. We prove the local-in-time unique existence of solutions to the Euler-Poincaré equations in $F^s_{p,r}(\R^d)$. Furthermore, we obtain that the data-to-solution of this equation is continuous but not uniformly continuous in these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12824 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness and no-uniform dependence for the Euler-Poincaré equations in Triebel-Lizorkin spaces Zhong, Yuanhua Lu, Jianzhong Li, Min Li, Jinlu Analysis of PDEs 35Q35 In this paper, we study the Cauchy problem of the Euler-Poincaré equations in $\R^d$ with initial data belonging to the Triebel-Lizorkin spaces. We prove the local-in-time unique existence of solutions to the Euler-Poincaré equations in $F^s_{p,r}(\R^d)$. Furthermore, we obtain that the data-to-solution of this equation is continuous but not uniformly continuous in these spaces. |
| title | Well-posedness and no-uniform dependence for the Euler-Poincaré equations in Triebel-Lizorkin spaces |
| topic | Analysis of PDEs 35Q35 |
| url | https://arxiv.org/abs/2403.12824 |