Global well-posedness for the full compressible Navier-Stokes equations

TL;DR

This paper proves the global existence and uniqueness of solutions for the full compressible Navier-Stokes equations with small initial data in Sobolev spaces, using Friedrich's method and compactness arguments.

Contribution

It establishes the first global well-posedness result for the full compressible Navier-Stokes equations in Sobolev spaces with small initial data.

Findings

Global well-posedness proved for small initial data

Solutions exist and are unique in Sobolev spaces

Method combines Friedrich's approach with compactness arguments

Abstract

In this paper, we mainly study the Cauchy problem for the full compressible Navier-Stokes equations in Sobolev spaces. We establish the global well-posedness of the equations with small initial data by using Friedrich's method and compactness arguments.