Global regularity of 3D generalized incompressible magnetohydrodynamic-α 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=32 with 34≤γ<32, then the 3D MHD-α model with fractional diffusion admits a unique global smooth solution.