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arXiv · 2512.18267

Well-posedness of the Euler system of gas dynamics

Eduard Feireisl·Maria Lukacova-Medvidova
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Abstract

We propose a new two-step selection criterion applicable to the dissipative measure--valued solutions of the Euler system of gas dynamics. The process consists of a successive maximisation of the entropy production rate and the total energy defect, i.e. maximisation of the turbulent energy. If the selected solution is a weak solution of the Euler system, then it is identified in the first step. Solutions selected in the second step are truly measure--valued maximising the energy defect. Accordingly, they are called turbulent solutions. The energy defect of turbulent solutions vanishes with growing time. The selected solutions depend in a Borel--measurable way on the initial data. In particular, they are almost continuously dependent on the initial data.

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Eduard Feireisl, Maria Lukacova-Medvidova. 2025-12-20. Well-posedness of the Euler system of gas dynamics. https://arxiv.org/abs/2512.18267

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