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

TL;DR

This paper proves the global existence of strong solutions for a non-isothermal ideal gas system using energy estimates and fixed point methods, covering both Sobolev and Besov space frameworks.

Contribution

It establishes the first comprehensive proof of global well-posedness for the non-isothermal ideal gas model in multiple functional spaces.

Findings

Global well-posedness in Sobolev space $H^2(R^3)$

Global well-posedness for small data in critical Besov space

Use of energy estimates and Banach fixed point theorem

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.