The Euler system of gas dynamics

TL;DR

This survey reviews recent advances in understanding the well and ill-posedness of the Euler system of gas dynamics, emphasizing the role of thermodynamics principles in solution selection.

Contribution

It synthesizes recent results on the limits of approximate solutions and the physical admissibility criteria for the Euler system.

Findings

Solutions can be obtained as limits of more complex models or numerical schemes.

Thermodynamics principles help identify unique physically admissible solutions.

The survey discusses conditions under which solutions are well-posed or ill-posed.

Abstract

This is a survey highlighting several recent results concerning well/ill posedness of the Euler system of gas dynamics. Solutions of the system are identified as limits of consistent approximations generated either by physically more complex problems, notably the Navier- Stokes-Fourier system, or by the approximate schemes in numerical experiments. The role of the fundamental principles encoded in the First and Second law of thermodynamics in identifying a unique physically admissible solution is examined.