Remarks on global regularity of 2D generalized MHD equations

In this paper, we investigate the global regularity of 2D generalized MHD equations, in which the dissipation term and magnetic diffusion term are $\nu (-\mathrm{\Delta }{)}^{\alpha }u$ and $\eta (-\mathrm{\Delta }{)}^{\beta }b$ respectively. Let $(u_{0}, b_{0})\in H^{s}$with$s\geq2$,itisshowedthatthesmoothsolution$(u(x,t),b(x,t))$isgloballyregularforthecase$ 0\leq\alpha\leq{1}{2}, \alpha+\beta > {3}{2}$.