Well-posedness for the Incompressible Hall-MHD Equations in Low Regularity Spaces

In this paper, we first establish the local well-posedness of strong solutions to the Cauchy problem of the incompressible viscous resistive Hall-MHD equations in Hs(R3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^s(\mathbb {R}^3)$$\end{document}(32<s≤52)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\frac{3}{2}< s\le \frac{5}{2})$$\end{document}, and then we prove that the local solution is global when the initial data is small enough.