This paper is devoted to the study of the Dirichlet problem for the compressible magnetohydrodynamic system with density-dependent viscosities \(\mu =const>0,\lambda =\rho ^\beta \) which was first introduced by Vaigant-Kazhikhov [18] in 1995. By assuming the endpoint case \(\beta =1\) in the radially spherical symmetric setting, we establish the global existence to strong solution of the two-dimensional system for any large initial data. This also improves the previous work of Huang-Yan [10] where they proved the similar result for \(\beta >1\) . Our main idea is to utilize the geometric structure of a 2D spherically symmetric disc and the Sobolev critical embedding inequality of spherically symmetric functions in 2D domains, as well as a refined estimate of the upper bound of the density.
