Global well-posedness for the incompressible MHD equations with variable viscosity and conductivity

In this paper, we consider the initial-boundary value problem of the incompressible MHD equations with variable viscosity and conductivity in a smooth bounded domain Ω⊂R3. We establish the global well-posedness of strong solutions in both non-vacuum and vacuum cases when the initial velocity field and magnetic field are suitably small in some sense with arbitrarily large initial density. In addition, we also get some results of the large-time behavior in both two cases. Our results generalize some previous results in some sense.