On the Cauchy problem of compressible full Hall-MHD equations

This paper is concerned with an initial value problem of the compressible full Hall-MHD equations in three-dimensional whole space. Both the global existence and the optimal decay rates of solutions are obtained, when the smooth initial data are sufficiently close to the non-vacuum equilibrium in H1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^1$$\end{document}. As a by-product of the uniform estimates, the vanishing limit of Hall coefficient is also justified.