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Maximal dissipation and well-posedness of the Euler system of gas dynamics

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arxiv 2501.05134 v2 pith:BAI3R2DE submitted 2025-01-09 math.AP

Eduard Feireisl , Ansgar Jüngel , Mária Lukáčová-Medvid'ová This is my paper · ORCID
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keywords solutioneulersystemcriteriondafermosdissipationdissipativemaximal
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A unified duality framework for barotropic, quantum and Korteweg fluids

    math.AP 2026-02 conditional novelty 6.0 of 10

    A common Brenier-type dual variational formulation is proved consistent, solvable, and gap-free for barotropic, quantum and Korteweg fluids, with a Dafermos principle for entropy dissipation.

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

    math.AP 2025-05 conditional novelty 6.0 of 10

    Oscillatory limits of consistent approximations to the Euler system always violate Dafermos' maximal entropy production criterion, because any maximal measure-valued solution must reduce to a Dirac measure.

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