Global Classical Solutions to Full Compressible Magnetohydrodynamic System with Large Oscillations and Vacuum in 3D Exterior Domains

TL;DR

This paper proves the global existence, uniqueness, and large-time behavior of classical solutions to the 3D full compressible magnetohydrodynamic system in exterior domains, allowing for vacuum states and large oscillations in initial data.

Contribution

It establishes the first global classical solutions for this complex system with vacuum and large oscillations in three-dimensional exterior domains.

Findings

Global existence and uniqueness of classical solutions.

Solutions exhibit specific large-time decay behavior.

Initial vacuum states are permitted in the analysis.

Abstract

The full compressible magnetohydrodynamic system in three-dimensional exterior domains is investigated. For the initial-boundary-value problem of this system with slip boundary condition for the velocity, adiabatic one for the temperature, and perfect one for the magnetic field, the global existence and uniqueness of classical solutions is established, under the condition that the initial data are of small energy but possibly large oscillations. In particular,the initial density and temperature are both allowed to vanish. Moreover, the large-time behavior of the classical solutions is also obtained.