Regularity and Energy Conservation for the Compressible Euler Equations

TL;DR

This paper establishes conditions on the regularity of solutions to compressible Euler equations that ensure energy conservation, extending previous methods used for incompressible flows.

Contribution

It provides new sufficient regularity conditions for energy conservation in compressible Euler equations using commutator estimates.

Findings

Regularity conditions for energy conservation established

Extension of Constantin et al.'s methods to compressible flows

Framework applicable to inhomogeneous and isentropic Euler systems

Abstract

We give sufficient conditions on the regularity of solutions to the inhomogeneous incompressible Euler and the compressible isentropic Euler systems in order for the energy to be conserved. Our strategy relies on commutator estimates similar to those employed by P. Constantin et al. for the homogeneous incompressible Euler equations.