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 (−Δ)α for 0<α<5∕4. Let μ, ν, u and b denote the viscosity coefficient, magnetic diffusivity, velocity field and magnetic field, respectively. It is shown that ‖(u,b)‖Hs (s>5∕2−α) is globally bounded as long as |μ−ν|(μ+ν)−1 and Ḣ52−2α-norm on (u0−b0) or (u0+b0) sufficiently small, which generalizes the previous result about large solutions in He et al. (2014).