Global well-posedness of 3D incompressible inhomogeneous magnetohydrodynamic equations

In this paper, we investigate the 3D inhomogeneous incompressible magneto-hydrodynamic (MHD) system. By the assumption of the smallness of initial velocity and magnetic fluids in the critical Besov space, the local and global well-posedness of 3D inhomogeneous incompressible equations is obtained. It improves some previous results of MHD equations by generalizing the range of exponent p in Besov spaces (B) over dot(p,1)(3/p-1) with 1 < p < 6. Besides, the initial density belongs to the critical Besov space B-q,1(3/q) with 1 < q < 6, and it is removed the additional restriction of 1 < q <= p, which is an important condition in some previous results for both 3D inhomogeneous incompressible Navier-Stokes equations and MHD system.