Large-Time Behavior for Compressible Navier–Stokes–Fourier System in the Whole Space

The current paper is devoted to the investigation of large-time behavior of the compressible Navier–Stokes–Fourier system in the whole space. Under the condition that ‖ρ‖Cα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Vert \rho \Vert _{C^\alpha } $$\end{document} and ‖ρ,T‖L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Vert \rho , T\Vert _{L^\infty }$$\end{document} possess uniform in time bound, we prove that the regular solutions converge to equilibrium with the optimal decay rate.