The global existence of strong solutions for a non-isothermal ideal gas system

We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space H2 (Double-struck capital R3) for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space B2,13/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{\boldsymbol{B}}_{\boldsymbol{2,1}}<^>{\boldsymbol{3/2}}$$\end{document} by showing that the linearized operator is a contraction mapping under the right circumstances.