Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2021; 58(6): 1521-1537

Published online November 30, 2021 https://doi.org/10.4134/BKMS.b210058

Copyright © The Korean Mathematical Society.

Global large solutions for the compressible magnetohydrodynamic system

Jinlu Li, Yanghai Yu, Weipeng Zhu

Gannan Normal University; Anhui Normal University; Foshan University

Abstract

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in $\R^d$ with $d\geq2$, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then the compressible magnetohydrodynamic system has a unique global solution. Our result improves the previous one by Danchin and Mucha \cite{Danchin2017} who considered the compressible Navier-Stokes equations.

Keywords: Compressible MHD system, global solution, Besov spaces

MSC numbers: Primary 35Q35, 76D03

Supported by: J. Li is supported by the National Natural Science Foundation of China (NNSFC) under Grants 11801090 and 12161004. Y. Yu is supported by NNSFC under Grant 12101011, by the Natural Science Foundation of Anhui Province under Grant 1908085QA05 and the PhD Scientific Research Start-up Foundation of Anhui Normal University. W. Zhu is partially supported by NNSFC under Grant 11901092 and Natural Science Foundation of Guangdong Province under Grant 2017A030310634.