Maximal entropy production principle and the Euler system of gas dynamics

Fuente: arXiv
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Autori principali: Chiodaroli, Elisabetta, Feireisl, Eduard, Kreml, Ondřej, Markfelder, Simon
Natura: Preprint
Pubblicazione: 2026
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author Chiodaroli, Elisabetta
Feireisl, Eduard
Kreml, Ondřej
Markfelder, Simon
author_facet Chiodaroli, Elisabetta
Feireisl, Eduard
Kreml, Ondřej
Markfelder, Simon
contents Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically relevant solution can be selected by maximizing the entropy production rate. Firstly, we present an example of Riemann initial data in 2-D, for which the standard self-similar solution fails to satisfy the maximal entropy production principle. Hence, maximizing the entropy production rate rules out the 1-D self-similar solution which intuitively seems to be the physically relevant solution in this context. Secondly, we show for a large class of initial data that there exist entropy admissible weak solutions with an arbitrary (non-decreasing) total entropy profile.
format Preprint
id arxiv_https___arxiv_org_abs_2605_26687
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Maximal entropy production principle and the Euler system of gas dynamics
Chiodaroli, Elisabetta
Feireisl, Eduard
Kreml, Ondřej
Markfelder, Simon
Analysis of PDEs
35L65, 35Q31, 76N10
Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically relevant solution can be selected by maximizing the entropy production rate. Firstly, we present an example of Riemann initial data in 2-D, for which the standard self-similar solution fails to satisfy the maximal entropy production principle. Hence, maximizing the entropy production rate rules out the 1-D self-similar solution which intuitively seems to be the physically relevant solution in this context. Secondly, we show for a large class of initial data that there exist entropy admissible weak solutions with an arbitrary (non-decreasing) total entropy profile.
title Maximal entropy production principle and the Euler system of gas dynamics
topic Analysis of PDEs
35L65, 35Q31, 76N10
url https://arxiv.org/abs/2605.26687