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Peer-reviewedCC BYArchive for Rational Mechanics and Analysis

Maximal Dissipation and Well-Posedness of the Euler System of Gas Dynamics

  • Eduard Feireisl1,2
  • Ansgar Jüngel1,3
  • Mária Lukáčová-Medviďová1,4
4 affiliations
  1. 1Erwin Schrödinger International Institute for Mathematics and Physics, Boltzmanngasse 9, 1090 Wien, Austria
  2. 2Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic
  3. 3Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstr. 8-10, 1040 Wien, Austria
  4. 4Institute of Mathematics, Johannes Gutenberg-University Mainz, Staudingerweg 9, 55 128 Mainz, Germany
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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.

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Cite

BibTeXRIS
BibTeX
@article{feireisl2026maximal,
  title = {{Maximal Dissipation and Well-Posedness of the Euler System of Gas Dynamics}},
  author = {Eduard Feireisl and Ansgar Jüngel and Mária Lukáčová-Medviďová},
  journal = {Archive for Rational Mechanics and Analysis},
  year = {2026},
  month = jun,
  doi = {10.1007/s00205-026-02205-4},
  url = {https://doi.org/10.1007/s00205-026-02205-4},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Maximal Dissipation and Well-Posedness of the Euler System of Gas Dynamics
AU  - Eduard Feireisl
AU  - Ansgar Jüngel
AU  - Mária Lukáčová-Medviďová
PY  - 2026
DA  - 2026/06/03
JO  - Archive for Rational Mechanics and Analysis
DO  - 10.1007/s00205-026-02205-4
UR  - https://doi.org/10.1007/s00205-026-02205-4
AB  - 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.
SN  - 0003-9527
SN  - 1432-0673
ER  -