Global Strong Solutions to the Compressible Magnetohydrodynamic Equations with Slip Boundary Conditions in a 3D Exterior Domain

TL;DR

This paper proves the global existence and uniqueness of classical solutions for the 3D compressible magnetohydrodynamic equations with slip boundary conditions in exterior domains, allowing large oscillations and vacuum states.

Contribution

It establishes the first global classical solutions with large oscillations and vacuum in a 3D exterior domain for the compressible MHD system.

Findings

Global existence and uniqueness of classical solutions

Solutions can have large oscillations and vacuum states

Analysis of large-time behavior of solutions

Abstract

In this paper we study the initial-boundary-value problem for the barotropic compressible magnetohydrodynamic system with slip boundary conditions in three-dimensional exterior domain. We establish the global existence and uniqueness of classical solutions to the exterior domain problem with the regular initial data that are of small energy but possibly large oscillations with constant state as far field which could be either vacuum or nonvacuum. In particular, the initial density of such a classical solution is allowed to have large oscillations contain vacuum states. Moreover, the large-time behavior of the solution is also shown.