Global existence and exponential decay of strong solutions for the 3D incompressible MHD equations with density-dependent viscosity coefficient

This paper deals with the 3D incompressible MHD equations with density-dependent viscosity in bounded domain. The global well-posedness of strong solutions is established in the vacuum cases, provided the assumption that $\overline{\rho }+\parallel H_0{\parallel }_{L^3}$ is suitably small with large velocity, which extends the recent work (Song in Z Angew Math Phys 69(2):23, 2018) to the global one. Furthermore, the exponential decay of the solution is also obtained.