Mixed 3D-2D asymptotics for the weak and strong solutions of the rotating magnetohydrodynamic system
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913933559857152 |
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| author | Charve, Frédéric Ngo, Van-Sang |
| author_facet | Charve, Frédéric Ngo, Van-Sang |
| contents | In this article, we consider the 3D-rotating magnetohydrodynamic (MHD) system when the initial velocity and magnetic field both feature some 2D-part (i.-e. depending only on the horizontal space variables). We prove for weak and strong solutions, that the limit system, when the Rossby number goes to zero (i.-e. for strong rotation), is a 2D-MHD system with three components. Moreover we are able to provide explicit global-in-time convergence rates thanks to adapted Strichartz estimates and with the help of an additional 3D magnetic field transported by the 2D limit velocity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed 3D-2D asymptotics for the weak and strong solutions of the rotating magnetohydrodynamic system Charve, Frédéric Ngo, Van-Sang Analysis of PDEs In this article, we consider the 3D-rotating magnetohydrodynamic (MHD) system when the initial velocity and magnetic field both feature some 2D-part (i.-e. depending only on the horizontal space variables). We prove for weak and strong solutions, that the limit system, when the Rossby number goes to zero (i.-e. for strong rotation), is a 2D-MHD system with three components. Moreover we are able to provide explicit global-in-time convergence rates thanks to adapted Strichartz estimates and with the help of an additional 3D magnetic field transported by the 2D limit velocity. |
| title | Mixed 3D-2D asymptotics for the weak and strong solutions of the rotating magnetohydrodynamic system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.06678 |