Global well-posedness for the 3-D incompressible inhomogeneous MHD system in the critical Besov spaces

In this paper, we study the Cauchy problem for the incompressible inhomogeneous magnetohydrodynamic (MHD) system in R3R3. We obtain the global existence of a unique solution for this system without any small conditions imposed on the third component of the initial velocity field and magnetic field in the critical Besov spaces. Our methods mainly rely upon the Fourier frequency localization and Bony's paraproduct decomposition.