A remark on global regularity of 2D generalized magnetohydrodynamic equations

In this paper we study the global regularity of the following 2D (two-dimensional) generalized magnetohydrodynamic equations { u t + u ⋅ ∇ u = − ∇ p + b ⋅ ∇ b − ν ( − Δ ) α u , b t + u ⋅ ∇ b = b ⋅ ∇ u − κ ( − Δ ) β b and get global regular solutions when 0 ≤ α < 1 / 2 , β ≥ 1 , 3 α + 2 β > 3 , which improves the results in [5]. In particular, we obtain the global regularity of the 2D generalized MHD when α = 0 and β > 3 2 .