Global existence of strong solution to non-isothermal ideal gas system

Abstract

This paper aims to establish the global existence of strong solutions to a non-isothermal ideal gas model. We first show global well-posedness in the Sobolev space $H^2({\mathbb{R}}^3)$ by using energy estimates. We then prove the global well-posedness for small-data solutions in the critical Besov space by using Banach's fixed point theorem.