Statistical solutions to the Euler system of gas dynamics

Eduard Feireisl

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arXiv · 2602.02205

Statistical solutions to the Euler system of gas dynamics

Eduard Feireisl

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Abstract

We consider the (complete) Euler system describing the motion of a compressible perfect fluid. We propose a platform suitable for constructing the statistical solutions. The main ingredients of our approach include: 1. The concept of dissipative (measure{valued) solution to the Euler system. 2. A single step selection procedure based on minimizing the Bregman divergence of a given solution to the maximal entropy equilibrium. 3. A construction of a Markov semigroup via push forward measures.

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Eduard Feireisl. 2026-02-02. Statistical solutions to the Euler system of gas dynamics. https://arxiv.org/abs/2602.02205

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