Global Smooth Solutions to the 3D Compressible Viscous Non-Isentropic Magnetohydrodynamic Flows Without Magnetic Diffusion

How to construct the global smooth solutions to the compressible viscous, non-isentropic, non-resistive magnetohydrodynamic equations in T3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {T}}^3$$\end{document} appears to be unknown. In this paper, we give a positive answer to this problem. More precisely, we prove a global stability result on perturbations near a strong background magnetic field to the 3D compressible viscous, non-isentropic, non-resistive magnetohydrodynamic equations. This stability result provides a significant example of the stabilizing effect of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit decay rate for the solutions to this nonlinear system.