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

2015/03/17 by Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Emil Wiedemann · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35A02 #msc:35B40 #msc:35L45 #msc:35Q31 #msc:35Q35 #msc:76N15 #msc:76T25 #physics.flu-dyn

paper · pdf · doi:10.1088/0951-7715/28/11/3873

arxiv created 2015/03/17 · openalex publication_date 2015/10/01 · arxiv updated 2015/10/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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.

Cited by

• Measure-valued solutions to the complete Euler system
• On the Low Mach Number Limit for the Compressible Euler System

Related

• Weak-strong uniqueness for measure-valued solutions
• Weak-Strong Uniqueness for the Isentropic Euler Equations with Possible Vacuum
• Weak-strong uniqueness in fluid dynamics
• Dissipative measure valued solutions for general conservation laws
• On the Selection of Measure-Valued Solutions for the Isentropic Euler System