Communications in Mathematical Sciences

Volume 19 (2021)

Number 6

Global existence of strong solutions to the planar compressible magnetohydrodynamic equations with large initial data in unbounded domains

Pages: 1655 – 1671



Boqiang Lü (College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, China)

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

Chengfeng Xiong (Institute of Applied Mathematics, Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences, Beijing, China)


In one-dimensional unbounded domains, we consider the equations of a planar compressible magnetohydrodynamic flow with constant viscosity and heat conductivity. More precisely, we prove the global existence of strong solutions to the magnetohydrodynamic equations with large initial data satisfying the same conditions as those of Kazhikhov’s theory in bounded domains [Kazhikhov, Boundary Value Problems for Equations of Mathematical Physics. Krasnoyarsk, 1987]. In particular, our result generalizes the Kazhikhov’s theory for the initial boundary value problem in bounded domains to the problem in unbounded domains.


magnetohydrodynamics, global strong solutions, large initial data, unbounded domains

2010 Mathematics Subject Classification

35Q35, 76N10

B. Lü is supported by NNSFC (11971217) and Jiangxi Provincial Natural Science Foundation (20202ACBL211002).

X. Shi is supported by NNSFC (11671027 &11471321).

Received 26 September 2020

Accepted 21 February 2021

Published 2 August 2021