Statistical solutions for the Navier-Stokes-Fourier system

TL;DR

This paper establishes a stability framework for strong solutions of the Navier-Stokes-Fourier system and introduces a novel concept of statistical solutions applicable beyond blow-up times.

Contribution

It provides a general stability result and develops a new concept of statistical solutions for the compressible Navier-Stokes-Fourier system.

Findings

Proves stability of strong solutions under certain conditions

Introduces statistical solutions extending beyond blow-up times

Enhances understanding of solution behavior in compressible fluid dynamics

Abstract

We show a general stability result in the framework of strong solutions of the Navier-Stokes-Fourier system describing the motion of a compressible viscous and heat conducting gas. As a corollary, we develop a concept of statistical solution in the class of regular solutions "beyond the blow up time".