Global strong solutions to the 3D incompressible MHD equations with density-dependent viscosity

This paper is concerned with the 3D incompressible MHD equations with density-dependent viscosity in smooth bounded domains. Through time-weighted a priori estimates, the global existence of strong solutions is established under the assumption that the initial energy is suitably small. This generalizes previous results for the 3D Navier-Stokes equations in Huang and Wang (2015) and Zhang (2015), which need ‖∇u0‖L2 to be small. The initial vacuum is allowed.