The failure of Hölder regularity of solutions for the Euler-Poincaré equations in Besov spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910314050617344 |
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| author | Qu, Guorong Li, Min |
| author_facet | Qu, Guorong Li, Min |
| contents | In this paper, we investigate the continuity of solution to the Euler-Poincaré equations. We show that the continuity of the solution cannot be improved to the Hölder continuity. That is, the solution of the Euler-Poincaré equations with initial data $u_0\in B^s_{p,r}$ belongs to $\mathcal{C}([0,T];B^s_{p,r}(\mathbb R^d))$ but not to $\mathcal{C}^α([0,T];B^s_{p,r}(\mathbb R^d))$ with any $α\in(0,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The failure of Hölder regularity of solutions for the Euler-Poincaré equations in Besov spaces Qu, Guorong Li, Min Analysis of PDEs 35Q35, 35B30 In this paper, we investigate the continuity of solution to the Euler-Poincaré equations. We show that the continuity of the solution cannot be improved to the Hölder continuity. That is, the solution of the Euler-Poincaré equations with initial data $u_0\in B^s_{p,r}$ belongs to $\mathcal{C}([0,T];B^s_{p,r}(\mathbb R^d))$ but not to $\mathcal{C}^α([0,T];B^s_{p,r}(\mathbb R^d))$ with any $α\in(0,1)$. |
| title | The failure of Hölder regularity of solutions for the Euler-Poincaré equations in Besov spaces |
| topic | Analysis of PDEs 35Q35, 35B30 |
| url | https://arxiv.org/abs/2402.00456 |