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=1β=1, in contrast to the previous result of α⩾12, we show that α>13 suffices in order for the solution pair of velocity and magnetic fields to remain smooth for all time.