Communications in Mathematical Sciences

Volume 22 (2024)

Number 3

Global strong solutions to the compressible magnetohydrodynamic equations with slip boundary conditions in a 3D exterior domain

Pages: 685 – 720

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n3.a4

Authors

Yazhou Chen (College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing, China)

Bin Huang (College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing, China)

Xiaoding Shi (College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing, China)

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 and can contain vacuum states. Moreover, the large-time behavior of the solution is also shown.

Keywords

compressible magnetohydrodynamic equations, global existence, exterior domain, slip boundary condition, vacuum

2010 Mathematics Subject Classification

35K65, 35Q55, 76N10, 76W05

Full Text (PDF format)

This research was partially supported by National Natural Science Foundation of China (Nos. 12171024, 11901025, 11971217, 11971020).

Received 25 January 2023

Received revised 1 August 2023

Accepted 17 August 2023

Published 4 March 2024