Weak-strong uniqueness for measure-valued solutions of some compressible fluid models. (8th October 2015)

• Record Type: Journal Article
• Authors: Gwiazda, Piotr; Świerczewska-Gwiazda, Agnieszka; Wiedemann, Emil
• Is Part Of: Nonlinearity. Volume 28:Number 11(2015:Nov.)
• Page Start: 3873
• Page End: 3890
• Publication Date: 2015-10-08
• Subjects: compressible Euler equations -- Savage–Hutter model -- weak-strong uniqueness -- measure-valued solutions -- dissipation in finite time; 35L45 (primary) -- 35A02 -- 35B40 -- 35Q35 -- 35Q31 -- 76N15 -- 76T25 (secondary); Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/11/3873
• Languages: English
• ISSNs: 0951-7715

Abstract

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.