On "discrete" solutions of the Euler system of gas dynamics

Anna Abbatiello; Eduard Feireisl

On "discrete" solutions of the Euler system of gas dynamics

Analysis of PDEs 2026-07-31 v1

Authors: Anna Abbatiello , Eduard Feireisl

Abstract

The method of Convex Integration has revealed a number of rather disturbing facts concerning well-posedness of the Euler system of gas dynamics. In particular, there is a dense set of "wild" initial data, for which the problem admits infinitely many physically admissible (entropy) weak solutions. We identify the class of initial data enjoying the following properties: (a) they give rise to a family of weak solutions with increasing entropy profiles; (b) the solutions are "discrete", meaning they attain only a finite number of constant states; (c) the solutions reach a prescribed terminal entropy profile when time goes to infinity.

Keywords

Euler system convex integration weak solutions entropy wild initial data discrete solutions

Cite

@article{arxiv.2608.00126,
  title  = {On "discrete" solutions of the Euler system of gas dynamics},
  author = {Anna Abbatiello and Eduard Feireisl},
  journal= {arXiv preprint arXiv:2608.00126},
  year   = {2026}
}