Large-Time Behavior for One-Dimensional Planar Compressible Magnetohydrodynamic Equations on Unbounded Domains
Abstract
Global existence and the large-time behavior of strong solutions to the one-dimensional planar compressible magnetohydrodynamic system in unbounded domains are investigated.The longitudinal viscosity is assumed to be a positive constant plus any nonnegative power of the density, or to depend on temperature through a power law. The heat conductivity is taken to be proportional to any nonnegative power of temperature, while the transverse viscosity and magnetic diffusivity are taken to be positive constants. Global existence, uniform-in-time estimates, and convergence to equilibrium are established without imposing any smallness conditions on the initial data. In the density-dependent case, any fixed nonnegative viscosity exponent is allowed; in the temperature-dependent case, the nonnegative viscosity exponent is required to be sufficiently small in terms of the initial data. An auxiliary elliptic equation is introduced to control magnetic-pressure oscillations through a square-root-in-time estimate. Combined with the estimates appropriate to each viscosity law, this yields uniform upper and positive lower bounds for the specific volume and temperature and asymptotic stability of the global strong solution.
Related
- Finite-Time Vanishing of Vacuum and Large-Time Behavior of the Multi-Dimensional Degenerate Compressible Navier-Stokes Equations with Large Spherically Symmetric Initial Data
- Asymptotic behavior of generic Riemann solutions to one-dimensional full compressible Navier-Stokes-Poisson equations
- Large time behavior of global solutions to one-dimensional non-isentropic compressible Navier-Stokes-Poisson equations with large initial data
- Existence and uniqueness of solutions for compressible magnetohydrodynamic equations with bounded density
- Global c1,α regularity and fine behavior at critical points for quasilinear elliptic equations with Orlicz growth and unbounded drift
BibTeX
@misc{li2026largetime,
title = {{Large-Time Behavior for One-Dimensional Planar Compressible Magnetohydrodynamic Equations on Unbounded Domains}},
author = {Jing Li and Ziyin Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20126},
eprint = {2609.20126},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20126},
}
RIS
TY - UNPB
TI - Large-Time Behavior for One-Dimensional Planar Compressible Magnetohydrodynamic Equations on Unbounded Domains
AU - Jing Li
AU - Ziyin Liu
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.20126
UR - https://arxiv.org/abs/2609.20126
AB - Global existence and the large-time behavior of strong solutions to the one-dimensional planar compressible magnetohydrodynamic system in unbounded domains are investigated.The longitudinal viscosity is assumed to be a positive constant plus any nonnegative power of the density, or to depend on temperature through a power law. The heat conductivity is taken to be proportional to any nonnegative power of temperature, while the transverse viscosity and magnetic diffusivity are taken to be positive constants. Global existence, uniform-in-time estimates, and convergence to equilibrium are established without imposing any smallness conditions on the initial data. In the density-dependent case, any fixed nonnegative viscosity exponent is allowed; in the temperature-dependent case, the nonnegative viscosity exponent is required to be sufficiently small in terms of the initial data. An auxiliary elliptic equation is introduced to control magnetic-pressure oscillations through a square-root-in-time estimate. Combined with the estimates appropriate to each viscosity law, this yields uniform upper and positive lower bounds for the specific volume and temperature and asymptotic stability of the global strong solution.
ER -