Global regularity of the 3D generalized MHD equations with only velocity dissipation

In this paper, we consider the global regularity of the three-dimensinal (3D) generalized magnetohydrodynamic (MHD) equations with only velocity dissipation in terms of fractional Laplacians. By the Galerkin approximation methods, the compactness and the energy method, we give a refined proof of the correlation theorem and prove the global existence and uniqueness of the strong solutions for any α ≥ 5/2