On the well-posedness of magnetohydrodynamics system with Hall and ion-slip in critical spaces

In this paper, we establish the global well-posedness of solutions for the magnetohydrodynamics with Hall and ion-slip effects in critical space by constructing the current function J=∇×B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J=\nabla \times B$$\end{document} as an additional unknown. Meanwhile, we consider the long-time behavior of the solutions and get some decay estimates.