Global large strong solution to the 3D incompressible MHD system with density-dependent viscosity

In this paper, we investigate the Dirichlet problem of three-dimen-sional non-homogeneous incompressible MHD equations with density-dependent viscosity. Under the assumption that the viscosity coefficient $ \mu(\rho) $ is a power function of the density $ \mu(\rho) = \mu\rho^{\alpha} $ with $ \alpha>1 $, we establish the global existence and uniqueness of strong solutions as long as the initial data are sufficiently large. This is the first result concerning the global existence of strong solutions to the non-homogeneous incompressible MHD equations in three dimensions with large data.