On action rate admissibility criteria

H. Gimperlein; M. Grinfeld; R. J. Knops; M. Slemrod

doi:10.1007/s00033-025-02705-5

On action rate admissibility criteria

H. Gimperlein^*
, M. Grinfeld
, R. J. Knops
, M. Slemrod

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

We formulate new admissibility criteria for initial value problems motivated by the least action principle. These are applied to a two-dimensional Riemann initial value problem for the isentropic compressible Euler fluid flow. It is shown that the criterion prefers the 2-shock solution to solutions obtained by convex integration by Chiodaroli and Kreml or to the hybrid solutions recently constructed by Markfelder and Pellhammer.

Original language	English
Article number	57
Journal	Zeitschrift für angewandte Mathematik und Physik ZAMP
Volume	77
Issue number	2
Early online date	12 Jan 2026
DOIs	https://doi.org/10.1007/s00033-025-02705-5
Publication status	Published - Feb 2026

Keywords

35C06
Weak solution
35D30
Convex integration
76N10
Admissible solution
35LQ35
Riemann problem
Entropy rate
35L65
Least action principle

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KW - 35D30

KW - Convex integration

KW - 76N10

KW - Admissible solution

KW - 35LQ35

KW - Riemann problem

KW - Entropy rate

KW - 35L65

KW - Least action principle

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ER -

On action rate admissibility criteria

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Keywords

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