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

IF 1.5 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2026-09-14 DOI:10.1007/s00021-026-01051-4

Simon Markfelder, Valentin Pellhammer

引用次数: 0

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.

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局部最小作用准则不能作为可压缩欧拉方程弱解的选择准则

众所周知，经典的可容许弱解（也称为弱熵解）的概念并不能恢复多维可压缩欧拉方程的唯一性。事实上，凸积分已经证明了可容许的弱解通常是高度非唯一的。这激发了额外的选择标准，旨在排除凸积分产生的反直觉的解决方案。在本文中，我们证明了H. Gimperlein， M. Grinfeld， R. J. Knops和M. Slemrod引入的局部最小作用准则不能作为一个合适的选择准则，因为它不能选择直观地期望具有物理相关性的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.