On the topology of the magnetic lines of large solutions to the Magnetohydrodynamic equations in $\mathbb{R}^3$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913071755165696 |
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| author | Lucà, Renato Peña, Claudia |
| author_facet | Lucà, Renato Peña, Claudia |
| contents | The purpose of this article is twofold: first, we introduce a new class of global strong solutions to the magnetohydrodynamic system in $\mathbb{R}^3$ with initial data $(u_0,b_0)$ of arbitrarily large size in any critical space. To do so, we impose a smallness condition on the difference $u_0-b_0$. Then we use this result to prove magnetic reconnection for a suitable class of (large) solutions. With this, we mean a change of topology of the integral lines of the magnetic field $b$ under the evolution. The proof relies on counting the number of hyperbolic critical points of the solutions, and this instance is structurally stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09340 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the topology of the magnetic lines of large solutions to the Magnetohydrodynamic equations in $\mathbb{R}^3$ Lucà, Renato Peña, Claudia Analysis of PDEs Mathematical Physics The purpose of this article is twofold: first, we introduce a new class of global strong solutions to the magnetohydrodynamic system in $\mathbb{R}^3$ with initial data $(u_0,b_0)$ of arbitrarily large size in any critical space. To do so, we impose a smallness condition on the difference $u_0-b_0$. Then we use this result to prove magnetic reconnection for a suitable class of (large) solutions. With this, we mean a change of topology of the integral lines of the magnetic field $b$ under the evolution. The proof relies on counting the number of hyperbolic critical points of the solutions, and this instance is structurally stable. |
| title | On the topology of the magnetic lines of large solutions to the Magnetohydrodynamic equations in $\mathbb{R}^3$ |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2505.09340 |