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.
Oscillatory approximations and maximum entropy principle for the Euler system of gas dynamics
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abstract
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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2026 1verdicts
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Maximal entropy production principle and the Euler system of gas dynamics
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.