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

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arxiv 2505.02070 v2 pith:YSGAXXQJ submitted 2025-05-04 math.AP

Eduard Feireisl , Mária Lukáčová-Medvid'ová , Changsheng Yu This is my paper · ORCID
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keywords oscillatoryapproximationsdafermosdynamicsentropyeulernumericalprinciple
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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.

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Cited by 3 Pith papers

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

  1. Maximal entropy production principle and the Euler system of gas dynamics

    math.AP 2026-05 unverdicted novelty 7.0 of 10

    For specific 2D Riemann data the self-similar solution fails the maximal entropy production principle, and entropy-admissible weak solutions exist with arbitrary non-decreasing total entropy profiles.

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

    math.AP 2026-07 conditional novelty 6.0 of 10

    For a dense set of initial data, the full Euler system admits infinitely many entropy-admissible weak solutions that take only finitely many constant states, with increasing entropy and prescribed terminal entropy.

  3. Numerical Study of Dissipative Weak Solutions for the Euler Equations of Gas Dynamics

    math.NA 2026-01 conditional novelty 5.0 of 10

    Different high-order numerical schemes for the compressible Euler equations yield different scheme-dependent dissipative weak solutions in oscillatory regimes, while order-averaged and time-averaged statistics look mo...

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