Oscillatory approximations and maximum entropy principle for the Euler system of gas dynamics

TL;DR

This paper demonstrates that oscillatory solutions of the Euler system of gas dynamics can violate the maximum entropy principle, with numerical evidence showing standard methods may produce such non-compliant solutions.

Contribution

It introduces a framework linking oscillatory approximations to entropy principles and highlights limitations of standard numerical methods in satisfying entropy criteria.

Findings

Oscillatory measure-valued solutions violate the maximal entropy production principle.

Standard numerical methods can produce oscillatory solutions that do not comply with the entropy criterion.

Numerical results illustrate the discrepancy between oscillatory solutions and entropy maximization.

Abstract

We show that the measure-valued solutions of the Euler system of gas dynamics generated by oscillatory sequences of consistent approximations violate the principle of maximal entropy production formulated by Dafermos. Numerical results illustrate that solutions obtained by standard numerical methods may be oscillatory and thus do not comply with the Dafermos criterion.