Maximal dissipation and well-posedness of the Euler system of gas dynamics
Analysis of PDEs
2025-01-23 v2
Abstract
We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible weak solution. In addition, we propose a simple, at most two step, selection procedure to identify a unique semigroup solution in the class of dissipative solutions to the Euler system. Finally, we introduce a refined version of Dafermos' criterion yielding a unique solution of the problem for any finite energy initial data.
Keywords
Cite
@article{arxiv.2501.05134,
title = {Maximal dissipation and well-posedness of the Euler system of gas dynamics},
author = {Eduard Feireisl and Ansgar Jüngel and Mária Lukáčová-Medvid'ová},
journal= {arXiv preprint arXiv:2501.05134},
year = {2025}
}