Global existence and stability of viscous Alfvén waves in the large-box limit for MHD systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918181068603392 |
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| author | Xu, Li Zhang, Jiahui |
| author_facet | Xu, Li Zhang, Jiahui |
| contents | This paper rigorously analyzes how the {\it large box limit} fundamentally alters the global existence theory and dynamics behavior of the incompressible magnetohydrodynamics (MHD) system with small viscosity/resistivity $(0<μ\ll 1)$ on periodic domains $Q_L=[-L,L]^3$, in presence of a strong background magnetic field. While the existence of global solutions (viscous Alfvén waves) on the whole space $\R^3$ was previously established in \cite{He-Xu-Yu}, such results cannot be expected for general finite periodic domains. We demonstrate that global solutions do exist on the torus $Q_L=[-L,L]^3$ precisely when the domain exceeds a size $L_μ>e^{\f1μ}$, providing the first quantitative characterization of the transition to infinite-domain-like behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global existence and stability of viscous Alfvén waves in the large-box limit for MHD systems Xu, Li Zhang, Jiahui Analysis of PDEs This paper rigorously analyzes how the {\it large box limit} fundamentally alters the global existence theory and dynamics behavior of the incompressible magnetohydrodynamics (MHD) system with small viscosity/resistivity $(0<μ\ll 1)$ on periodic domains $Q_L=[-L,L]^3$, in presence of a strong background magnetic field. While the existence of global solutions (viscous Alfvén waves) on the whole space $\R^3$ was previously established in \cite{He-Xu-Yu}, such results cannot be expected for general finite periodic domains. We demonstrate that global solutions do exist on the torus $Q_L=[-L,L]^3$ precisely when the domain exceeds a size $L_μ>e^{\f1μ}$, providing the first quantitative characterization of the transition to infinite-domain-like behavior. |
| title | Global existence and stability of viscous Alfvén waves in the large-box limit for MHD systems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.20086 |