Global regularity for the Cauchy problem of three-dimensional compressible magnetohydrodynamics equations

In this paper, we study the Cauchy problem for the three-dimensional compressible magnetohydrodynamics equations. We establish a blowup criterion for global regularity of strong solutions, which depends only on density and magnetic field. In addition, the initial data can be arbitrarily large and contain vacuum states. The proof is based on the new a priori estimates for three-dimensional compressible magnetohydrodynamics equations.