Remarks on global regularity of 2D generalized MHD equations

Abstract: In this paper, we investigate the global regularity of 2D generalized MHD equations, in which the dissipation term and magnetic diffusion term are $\nu(-\Delta)^\alpha u$ and $\eta (-\Delta)^\beta b$ respectively. Let $(u_{0}, b_{0})\in H^{s}$ with $s\geq2$, it is showed that the smooth solution $(u(x,t),b(x,t))$ is globally regular for the case $ 0\leq\alpha\leq{1}{2}, \alpha+\beta > {3}{2}$.