Global strong solutions for 3D viscous incompressible heat conducting magnetohydrodynamic flows with non-negative density

We study an initial boundary value problem for the nonhomogeneous heat conducting magnetohydrodynamic fluids with non-negative density. Firstly, it is shown that for the initial density allowing vacuum, the strong solution to the problem exists globally if the gradients of velocity and magnetic field satisfy parallel to del u parallel to(L4(0,T;L2)) + parallel to del b parallel to(L4(0,T;L2)) < infinity. Then, under some smallness condition, we prove that there is a unique global strong solution to the 3D viscous incompressible heat conducting magnetohydrodynamic flows. Our method relies upon the delicate energy estimates and regularity properties of Stokes system and elliptic equations. (C) 2016 Elsevier Inc. All rights reserved.