Global stability and asymptotic behavior for the incompressible MHD equations without viscosity or magnetic diffusion
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909873847926784 |
|---|---|
| author | Bie, Qunyi Fang, Hui Zhou, Yanping |
| author_facet | Bie, Qunyi Fang, Hui Zhou, Yanping |
| contents | Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification of this effect for the $n$-dimensional incompressible magnetohydrodynamic equations with partial diffusion on periodic domains. We establish the global stability and derive explicit decay rates for perturbations around an equilibrium magnetic field satisfying the Diophantine condition. Our results yield the \textit{effective decay rates in all intermediate Sobolev norms} and \textit{significantly relax the regularity requirements} on the initial data compared with previous works (\textit{Sci. China Math.} 41:1--10, 2022; \textit{J. Differ. Equ.} 374:267--278, 2023; \textit{Calc. Var. Partial Differ. Equ.} 63:191, 2024). Furthermore, the analytical framework developed here is dimension-independent and can be flexibly adapted to other fluid models with partial dissipation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global stability and asymptotic behavior for the incompressible MHD equations without viscosity or magnetic diffusion Bie, Qunyi Fang, Hui Zhou, Yanping Analysis of PDEs Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification of this effect for the $n$-dimensional incompressible magnetohydrodynamic equations with partial diffusion on periodic domains. We establish the global stability and derive explicit decay rates for perturbations around an equilibrium magnetic field satisfying the Diophantine condition. Our results yield the \textit{effective decay rates in all intermediate Sobolev norms} and \textit{significantly relax the regularity requirements} on the initial data compared with previous works (\textit{Sci. China Math.} 41:1--10, 2022; \textit{J. Differ. Equ.} 374:267--278, 2023; \textit{Calc. Var. Partial Differ. Equ.} 63:191, 2024). Furthermore, the analytical framework developed here is dimension-independent and can be flexibly adapted to other fluid models with partial dissipation. |
| title | Global stability and asymptotic behavior for the incompressible MHD equations without viscosity or magnetic diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.24338 |