Magnetic Stabilization of Compressible Flows: Global Existence in 3D Inviscid Non-Isentropic MHD Equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913933119455232 |
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| author | Wu, Jiahong Xu, Fuyi Zhai, Xiaoping |
| author_facet | Wu, Jiahong Xu, Fuyi Zhai, Xiaoping |
| contents | Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the inviscid compressible flow is coupled with the magnetic field in the 3D inviscid non-isentropic compressible magnetohydrodynamic (MHD) equations in $\mathbb{T}^3$, this paper rules out finite-time blowup and establishes the global existence of smooth and stable solutions near a suitable background magnetic field. This result rigorously confirms the stabilizing phenomenon observed in physical experiments involving electrically conducting fluids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magnetic Stabilization of Compressible Flows: Global Existence in 3D Inviscid Non-Isentropic MHD Equations Wu, Jiahong Xu, Fuyi Zhai, Xiaoping Analysis of PDEs Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the inviscid compressible flow is coupled with the magnetic field in the 3D inviscid non-isentropic compressible magnetohydrodynamic (MHD) equations in $\mathbb{T}^3$, this paper rules out finite-time blowup and establishes the global existence of smooth and stable solutions near a suitable background magnetic field. This result rigorously confirms the stabilizing phenomenon observed in physical experiments involving electrically conducting fluids. |
| title | Magnetic Stabilization of Compressible Flows: Global Existence in 3D Inviscid Non-Isentropic MHD Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.00888 |