Weak-strong uniqueness for measure-valued solutions of some compressible fluid models

TL;DR

This paper establishes weak-strong uniqueness for measure-valued solutions of certain compressible fluid models, including the isentropic Euler equations and the Savage-Hutter model, with additional results on momentum dissipation.

Contribution

It proves weak-strong uniqueness for measure-valued solutions in these models and demonstrates finite-time momentum dissipation for the Savage-Hutter system.

Findings

Weak-strong uniqueness holds for the isentropic Euler equations in any dimension.

Complete dissipation of momentum occurs in finite time for the Savage-Hutter model.

Provides rigorous justification for assumptions used in engineering and numerical studies.

Abstract

We prove weak-strong uniqueness in the class of admissible measure-valued solutions for the isentropic Euler equations in any space dimension and for the Savage-Hutter model of granular flows in one and two space dimensions. For the latter system, we also show the complete dissipation of momentum in finite time, thus rigorously justifying an assumption that has been made in the engineering and numerical literature.