Incompressible limits at large Mach number for a reduced compressible MHD system
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arXiv
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| Format: | Preprint |
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2025
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| author | Fanelli, Francesco Kwon, Young-Sam Wróblewska-Kamińska, Aneta |
| author_facet | Fanelli, Francesco Kwon, Young-Sam Wróblewska-Kamińska, Aneta |
| contents | This paper studies a singular limit problem for a reduced model for compressible non-resistive MHD which was first introduced in \cite{Li-Sun_JDE, Li-Sun} in a two-dimensional setting. This system can also be related to a certain class of two-fluid models. By a suitable rescaling of the magnetic pressure in terms of some parameter $\varepsilon>0$, by letting $\varepsilon\to 0$ we perform the incompressible limit while keeping the Mach number of order $O(1)$.
The study is conducted in the framework of global in time finite energy weak solutions and for ill-prepared initial data. We also consider a similar problem in presence of a strong Coriolis term. The key ingredient of the proof, based on a compensated compactness argument, is the use of the transport equation (well-known in the context of two-fluid models) underlying the dynamics. Thanks to it, and differently from previous studies about the incompressible limit, we are able to identify the asymptotics of the terms of order $O(\varepsilon)$ and to characterise their dynamics; such an information is in fact crucial to obtain a closed system in the limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incompressible limits at large Mach number for a reduced compressible MHD system Fanelli, Francesco Kwon, Young-Sam Wróblewska-Kamińska, Aneta Analysis of PDEs This paper studies a singular limit problem for a reduced model for compressible non-resistive MHD which was first introduced in \cite{Li-Sun_JDE, Li-Sun} in a two-dimensional setting. This system can also be related to a certain class of two-fluid models. By a suitable rescaling of the magnetic pressure in terms of some parameter $\varepsilon>0$, by letting $\varepsilon\to 0$ we perform the incompressible limit while keeping the Mach number of order $O(1)$. The study is conducted in the framework of global in time finite energy weak solutions and for ill-prepared initial data. We also consider a similar problem in presence of a strong Coriolis term. The key ingredient of the proof, based on a compensated compactness argument, is the use of the transport equation (well-known in the context of two-fluid models) underlying the dynamics. Thanks to it, and differently from previous studies about the incompressible limit, we are able to identify the asymptotics of the terms of order $O(\varepsilon)$ and to characterise their dynamics; such an information is in fact crucial to obtain a closed system in the limit. |
| title | Incompressible limits at large Mach number for a reduced compressible MHD system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.18078 |