On the global regularity of two-dimensional generalized magnetohydrodynamics system

We study the two-dimensional generalized magnetohydrodynamics system with dissipation and diffusion in terms of fractional Laplacians. In particular, in the case where the diffusion term has the power β = 1 , in contrast to the previous result of α ⩾ 1 2 , we show that α > 1 3 suffices in order for the solution pair of velocity and magnetic fields to remain smooth for all time.