Global Cauchy problem of 2D generalized magnetohydrodynamic equations

In this paper we prove the global-in-time existence of smooth solutions of the 2D generalized magnetohydrodynamic equations with zero viscosity, when the power of the Laplacian operator -Delta in the dissipation term of the induction equation is between 1 and 2. We also show a regularity criterion on the direction of the magnetic field b(0) := b/vertical bar b vertical bar when beta = 1. (C) 2014 Elsevier Inc. All rights reserved.