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

Abstract

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.