Dynamics of Partial Differential Equations

Volume 17 (2020)

Number 1

Global solutions of the 3D compressible MHD system in a bounded domain

Pages: 61 – 73

DOI: https://dx.doi.org/10.4310/DPDE.2020.v17.n1.a3

Authors

Jishan Fan (Department of Applied Mathematics, Nanjing Forestry University, Nanjing, China)

Lulu Jing (Center for Information, Nanjing Forestry University, Nanjing, China)

Gen Nakamura (Department of Mathematics, Hokkaido University, Sapporo, Japan)

Tong Tang (Department of Mathematics, College of Sciences, Hohai University, Nanjing, China)

Abstract

In this paper we consider the 3D compressible MHD system in a bounded domain. We first prove a regularity criterion and then use it and the bootstrap argument to show the well-posedness of global small solutions. It is important to point out that we do not need the smallness of initial velocity, so we improve the previous results in some senses.

Keywords

MHD, regularity criterion, bounded domain, strong solutions

2010 Mathematics Subject Classification

35Q30, 35Q35, 76D03

Full Text (PDF format)

J. Fan is partially supported by NSFC (No. 11971234).

Tong Tang is partially supported by NSFC (No. 11801138).

Received 5 May 2019

Published 18 February 2020