Global solutions to 3D incompressible rotational MHD system

This study investigates the Cauchy problem of an incompressible magnetohydrodynamic system in the rotational framework. Under the assumption that the rotation speed is sufficiently large, the Cauchy problem is shown to be globally well-posed in Hs(R3)×(L2∩Lq)(R3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^{s}({{\mathbb {R}}}^3)\times (L^2\cap L^q) ({{\mathbb {R}}}^3)$$\end{document} for 12<s<34\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}<s < \frac{3}{4}$$\end{document} and 3<q<min{63-2s,276+4s}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3<q < \min \{\frac{6}{3-2s},\,\frac{27}{6 + 4s}\}$$\end{document}.