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

Abstract

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 $${x^{1 - 2\alpha }} = \left\{ {u \in D'\left( {{R^3}} \right):{{\int_{{R^3}} {\left| \xi \right|} }^{1 - 2\alpha }}\left| {\hat u\left( \xi \right)} \right|d\xi < + \infty } \right\}$$ . In addition, we also give Gevrey class regularity of the solution.