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{ut+u⋅∇u=−∇p+b⋅∇b−ν(−Δ)αu,bt+u⋅∇b=b⋅∇u−κ(−Δ)βb and get global regular solutions when 0≤α<1/2, β≥1, 3α+2β>3, which improves the results in [5]. In particular, we obtain the global regularity of the 2D generalized MHD when α=0 and β>32.