The Euler system of gas dynamics

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.