Global regularity for the 3D MHD system with partial viscosity and magnetic diffusion terms

This paper is concerned with the Cauchy problem of the incompressible magnetohydrodynamic system with partial viscosity and magnetic diffusion terms in the three-dimensional whole space. The existence of the global strong solution (u,b) is obtained, provided that the initial data (‖u0‖L22+‖b0‖L22)(‖∇u0‖L22+‖∇b0‖L22) is suitably small.