Global regularity to the 3D generalized MHD equations with large initial data

This paper considers the global regularity to the 3D generalized MHD equations with the fractional dissipation and magnetic diffusion (-Delta)(alpha) for 0 < alpha < 5/4. Let mu, v, u and b denote the viscosity coefficient, magnetic diffusivity, velocity field and magnetic field, respectively. It is shown that parallel to(u, b)parallel to(s)(H) (s > 5/2 alpha) is globally bounded as long as vertical bar mu - nu vertical bar ( mu + nu)(-1) and (H)(5/2 - alpha) over dot -norm on (u(0) - b(0)) or (u(0) + b(0)) sufficiently small, which generalizes the previous result about large solutions in He et al. (2014). (C) 2017 Elsevier Ltd. All rights reserved.