Work

The Local Least Action Criterion Fails as a Selection Criterion for Weak Solutions of the Compressible Euler Equations

Year: 2026

Type: article

Abstract: It is now well known that the classical notion of admissible weak solutions (also known as weak entropy solutions) does not restore uniqueness for the multi-dimensional compressible Euler equations. Indeed, convex integration has shown that admissible weak solutions are in general highly non-unique. This has motivated additional selection criteria intended to rule out the counterintuitive solutions generated by convex integration. In this paper we prove that the local least action criterion introduced by H. Gimperlein, M. Grinfeld, R. J. Knops and M. Slemrod does not serve as a proper selection criterion, since it fails to select the solution that is intuitively expected to be physically relevant.

Source: Journal of Mathematical Fluid Mechanics

DOI: 10.1007/s00021-026-01051-4

Authors: Simon Markfelder, Valentin Pellhammer

Institutions: University of Konstanz, University of Hohenheim

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funder: Deutsche Forschungsgemeinschaft