On the topology of the magnetic lines of solutions of the MHD equations
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912065157857280 |
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| author | Ciampa, Gennaro |
| author_facet | Ciampa, Gennaro |
| contents | We construct examples of smooth periodic solutions to the Magnetohydrodynamic equations in dimension 2 with positive resistivity for which the topology of the magnetic lines changes under the flow. By Alfvén's theorem this is known to be impossible in the ideal case (resistivity = 0). In the resistive case the reconnection of the magnetic lines is known to occur and has deep physical implications, being responsible for many dynamic phenomena in astrophysics. The construction is a simplified proof of [3] and in addition we consider the case of the forced system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02999 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the topology of the magnetic lines of solutions of the MHD equations Ciampa, Gennaro Analysis of PDEs We construct examples of smooth periodic solutions to the Magnetohydrodynamic equations in dimension 2 with positive resistivity for which the topology of the magnetic lines changes under the flow. By Alfvén's theorem this is known to be impossible in the ideal case (resistivity = 0). In the resistive case the reconnection of the magnetic lines is known to occur and has deep physical implications, being responsible for many dynamic phenomena in astrophysics. The construction is a simplified proof of [3] and in addition we consider the case of the forced system. |
| title | On the topology of the magnetic lines of solutions of the MHD equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2303.02999 |