Global regularity of 3D generalized incompressible magnetohydrodynamic- model

In this paper, we prove the global regularity to the Cauchy problem of 3D incompressible magnetohydrodynamic- α (MHD- α ) model with fractional diffusion. We prove that if the exponents γ and β satisfy γ + β = 3 2 with 3 4 ≤ γ < 3 2 , then the 3D MHD- α model with fractional diffusion admits a unique global smooth solution.