Global strong solutions to the aligned 2.5D non-resistive full MHD system with high temperature and a strong magnetic field
Abstract
We study the Cauchy problem for an aligned vertical-field reduction of the full compressible non-resistive MHD equations in two space variables. The shear and bulk viscosities are proportional to θα, and the heat conductivity is proportional to θβ. For 2<α<β<α+2, we prove global existence and uniqueness of strong solutions when the background temperature and the comparable magnetic background are sufficiently large, while the positive density background is fixed. The velocity and temperature perturbations belong initially to H2, and the transported magnetic perturbation belongs to H1∩ D1,4; their absolute norms may be bounded by an arbitrary fixed constant. Alignment is essential and implies a small density perturbation relative to the magnetic background. Our proof combines relative energy estimates, uniform in the background temperature and magnetic field, with coupled estimates for the material derivatives of the velocity and temperature. These bounds control the source terms in the damped magnetic-gradient equation, allowing us to close the global a priori estimates without a separate large-time decay assumption. We construct the global strong solution by smooth approximation and Sobolev energy estimates for the approximating solutions, and prove uniqueness by an energy estimate for the difference of two solutions.
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BibTeX
@misc{li2026global,
title = {{Global strong solutions to the aligned 2.5D non-resistive full MHD system with high temperature and a strong magnetic field}},
author = {Yachun Li and Zixuan Qu and Zhaoyang Shang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26547},
eprint = {2610.26547},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26547},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global strong solutions to the aligned 2.5D non-resistive full MHD system with high temperature and a strong magnetic field
AU - Yachun Li
AU - Zixuan Qu
AU - Zhaoyang Shang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26547
UR - https://arxiv.org/abs/2610.26547
AB - We study the Cauchy problem for an aligned vertical-field reduction of the full compressible non-resistive MHD equations in two space variables. The shear and bulk viscosities are proportional to θ^α, and the heat conductivity is proportional to θ^β. For 2<α<β<α+2, we prove global existence and uniqueness of strong solutions when the background temperature and the comparable magnetic background are sufficiently large, while the positive density background is fixed. The velocity and temperature perturbations belong initially to H^2, and the transported magnetic perturbation belongs to H^1∩ D^1,4; their absolute norms may be bounded by an arbitrary fixed constant. Alignment is essential and implies a small density perturbation relative to the magnetic background. Our proof combines relative energy estimates, uniform in the background temperature and magnetic field, with coupled estimates for the material derivatives of the velocity and temperature. These bounds control the source terms in the damped magnetic-gradient equation, allowing us to close the global a priori estimates without a separate large-time decay assumption. We construct the global strong solution by smooth approximation and Sobolev energy estimates for the approximating solutions, and prove uniqueness by an energy estimate for the difference of two solutions.
ER -