Global solutions for the 3-D incompressible nonhomogeneous MHD equations

In this article, we establish the global well-posedness to the 3-D incompressible non-homogeneous magnetohydrodynamics (MHD) equations for a class of large velocity fields and magnetic fields in critical Besov spaces. We improve recent results by Chen et al. (2015) and Zhai et al. (2015) by extending the validity range of the parameters related to the integrability from 1