Global well-posedness of the 3D generalized rotating magnetohydrodynamics equations

In this paper, we establish the global well-posedness of the generalized rotating magnetohydrodynamics equations if the initial data are in X1−2α defined by x1−2α={u∈D′(R3):∫R3|ξ|1−2α|u^(ξ)|dξ<+∞}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x^{1 - 2\alpha }} = \left\{ {u \in D'\left( {{R^3}} \right):{{\int_{{R^3}} {\left| \xi \right|} }^{1 - 2\alpha }}\left| {\hat u\left( \xi \right)} \right|d\xi < + \infty } \right\}$$\end{document}. In addition, we also give Gevrey class regularity of the solution.