Global Stability of 3D Compressible Non-Resistive MHD: Hidden Damping and Rational Background Fields
Abstract
We prove the global well-posedness and nonlinear stability of classical solutions to the three-dimensional compressible viscous, non-resistive MHD system on π3 near the equilibrium (1,0,e3), for small x3-symmetric perturbations and without any Diophantine condition on the background magnetic field. The central obstruction is the x3-independent sector, in which the density and the magnetic field possess no dissipation, no damping, and no decay. We overcome it by exhibiting a hidden wave structure for the exact total pressure π=P(1+a)+B3+1/2|B|2, the averaged pair (uΜ ,πΜ ) obeys a closed system, and πΜ satisfies a strongly damped wave equation whose principal wave part propagates at the fast magnetosonic speed and whose non-parabolic branch damps at a rate that involves no gain of derivatives. This hidden damping substitutes for the missing magnetic dissipation, and simultaneously absorbs the magnetic pressure 1/2β|B|2, the main obstruction created by compressibility. Together with a damped wave structure for the oscillatory sector and space-time weighted energy functionals with shifted time weights, this yields global existence, uniform stability, and explicit polynomial decay rates.
Related
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BibTeX
@misc{li2026global,
title = {{Global Stability of 3D Compressible Non-Resistive MHD: Hidden Damping and Rational Background Fields}},
author = {Lin-An Li and Qian Li and Jiahong Wu and Xiaojing Xu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14244},
eprint = {2609.14244},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14244},
}
RIS
TY - UNPB
TI - Global Stability of 3D Compressible Non-Resistive MHD: Hidden Damping and Rational Background Fields
AU - Lin-An Li
AU - Qian Li
AU - Jiahong Wu
AU - Xiaojing Xu
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14244
UR - https://arxiv.org/abs/2609.14244
AB - We prove the global well-posedness and nonlinear stability of classical solutions to the three-dimensional compressible viscous, non-resistive MHD system on π^3 near the equilibrium (1,0,e_3), for small x_3-symmetric perturbations and without any Diophantine condition on the background magnetic field. The central obstruction is the x_3-independent sector, in which the density and the magnetic field possess no dissipation, no damping, and no decay. We overcome it by exhibiting a hidden wave structure for the exact total pressure π=P(1+a)+B_3+1/2|B|^2, the averaged pair (uΜ
,πΜ
) obeys a closed system, and πΜ
satisfies a strongly damped wave equation whose principal wave part propagates at the fast magnetosonic speed and whose non-parabolic branch damps at a rate that involves no gain of derivatives. This hidden damping substitutes for the missing magnetic dissipation, and simultaneously absorbs the magnetic pressure 1/2β|B|^2, the main obstruction created by compressibility. Together with a damped wave structure for the oscillatory sector and space-time weighted energy functionals with shifted time weights, this yields global existence, uniform stability, and explicit polynomial decay rates.
ER -