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 Global large solutions for the compressible magnetohydrodynamic system Bull. Korean Math. Soc.Published online August 20, 2021 Jinlu Li, Yanghai Yu, and Weipeng Zhu Gannan Normal University; Anhui Normal University; Guangzhou 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 due to Danchin and Mucha \cite{Danchin2017}(Adv. Math., 2017) who considered the compressible Navier-Stokes equations. Keywords : Compressible MHD system; Global solution; Besov spaces. MSC numbers : 35Q35; 76D03 Full-Text :