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 beta = 1, in contrast to the previous result of alpha >= 1/2, we show that alpha > 1/3 suffices in order for the solution pair of velocity and magnetic fields to remain smooth for all time. (C) 2014 Elsevier Inc. All rights reserved.