The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System

In this paper, we are interested in the global well-posedness of the strong solutions to the Cauchy problem on the compressible magnetohydrodynamics system with Hall effect. Moreover, we establish the convergence rates of the above solutions trending towards the constant equilibrium (& rho; over bar ,0,B over bar )\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$({\bar{\rho }},0,\bar{\textbf{B}})$$\end{document}, provided that the initial perturbation belonging to H3(R3)& AND;B2,& INFIN;-s(R3)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H<^>3({\mathbb {R}}<^>3) \cap B_{2, \infty }<^>{-s}({\mathbb {R}}<^>3)$$\end{document} for s & ISIN;(0,32]\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$s \in (0,\frac{3}{2}]$$\end{document} is sufficiently small.