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arXiv · 2211.06231

Global small solutions to the 3D compressible viscous non-resistive MHD system

Jiahong Wu·Xiaoping Zhai
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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 $\mathbb R^3$ or the periodic box $\mathbb T^3$ 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.

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Jiahong Wu, Xiaoping Zhai. 2023-07-18. Global small solutions to the 3D compressible viscous non-resistive MHD system. https://arxiv.org/abs/2211.06231

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