Energy conservation law for weak solutions of the full compressible Navier-Stokes equations

TL;DR

This paper establishes a sufficient condition under which weak solutions of the full compressible Navier-Stokes equations conserve energy, relaxing previous regularity requirements for density.

Contribution

It introduces a new integrability condition ensuring energy conservation for weak solutions, broadening the class of solutions that satisfy the energy law.

Findings

Weak solutions with the new integrability condition conserve energy

Relaxed regularity conditions for density compared to prior results

Applicable to solutions constructed by Feireisl

Abstract

We consider a sufficient condition for the energy conservation law of a weak solution for the full compressible Navier-Stokes equations on the torus. We prove that a weak solution constructed by Feireisl with certain integrability conditions conserve the energy. Our assumption relaxes the regularity condition for the density compared with existing results.