Global Strong Solutions to the Cauchy Problem of Three-dimensional Isentropic Magnetohydrodynamics Equations with Large Initial Data

We consider the Cauchy problem to the three-dimensional isentropic compressible Magnetohydrodynamics (MHD) system with density-dependent viscosities. When the initial density is linearly equivalent to a large constant state, we prove that strong solutions exist globally in time, and there is no restriction on the size of the initial velocity and initial magnetic field. As far as we know, this is the first result on the global well-posedness of density-dependent viscosities with large initial data for 3D compressible MHD equations.