Global Well-Posedness for Planar Compressible Magnetohydrodynamics with Degenerate Viscosity on Unbounded Domains
Abstract
The one-dimensional planar compressible magnetohydrodynamic system is studied on unbounded domains. The longitudinal viscosity obeys a power law of the specific volume, which permits it to degenerate as the density approaches vacuum, and the heat conductivity follows a power law of the temperature. For any fixed non-negative exponent in the heat conductivity term, the existence and uniqueness of global strong solutions are established for arbitrarily large initial data, provided that the positive exponent for viscosity is sufficiently small. The specific volume and temperature possess time-independent upper and lower bounds. Moreover, for each admissible viscosity exponent, the solution converges uniformly in space to the equilibrium state as time tends to infinity.
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BibTeX
@misc{li2026global,
title = {{Global Well-Posedness for Planar Compressible Magnetohydrodynamics with Degenerate Viscosity on Unbounded Domains}},
author = {Shixuan Li and Hongyu Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00278},
eprint = {2610.00278},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00278},
}
RIS
TY - UNPB
TI - Global Well-Posedness for Planar Compressible Magnetohydrodynamics with Degenerate Viscosity on Unbounded Domains
AU - Shixuan Li
AU - Hongyu Wang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00278
UR - https://arxiv.org/abs/2610.00278
AB - The one-dimensional planar compressible magnetohydrodynamic system is studied on unbounded domains. The longitudinal viscosity obeys a power law of the specific volume, which permits it to degenerate as the density approaches vacuum, and the heat conductivity follows a power law of the temperature. For any fixed non-negative exponent in the heat conductivity term, the existence and uniqueness of global strong solutions are established for arbitrarily large initial data, provided that the positive exponent for viscosity is sufficiently small. The specific volume and temperature possess time-independent upper and lower bounds. Moreover, for each admissible viscosity exponent, the solution converges uniformly in space to the equilibrium state as time tends to infinity.
ER -