Global small solutions to the 3D compressible viscous non-resistive MHD system
Analysis of PDEs
2023-07-19 v2
Abstract
Whether or not smooth solutions to the 3D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion are always global in time remains an extremely challenging open problem. No global well-posedness or stability result is currently available for this 3D MHD system in the whole space or the periodic box even when the initial data is small or near a steady-state solution. This paper presents a global existence and stability result for smooth solutions to this 3D MHD system near any background magnetic field satisfying a Diophantine condition.
Keywords
Cite
@article{arxiv.2211.06231,
title = {Global small solutions to the 3D compressible viscous non-resistive MHD system},
author = {Jiahong Wu and Xiaoping Zhai},
journal= {arXiv preprint arXiv:2211.06231},
year = {2023}
}
Comments
The final published version. To appear in Math. Models Methods Appl. Sci