Compressible Euler equations with general pressure law
type: Item
instance of: scholarly article
title: Compressible Euler equations with general pressure law
zbMATH Open document ID: 0970.76082
author: Philippe G. LeFloch
author: Gui-Qiang Chen
published in: Archive for Rational Mechanics and Analysis
publication date: 2001-10-04T00:00:00Z
review text: The authors consider one-dimensional Euler equations of isentropic compressible fluid, and prove the existence of entropy solutions. Pressure is a general function of density. The only restriction is that the pressure law corresponds to a polytropic perfect gas asymptotically near vacuum. Approximate solutions are constructed by the vanishing artificial viscosity method or by the Lax-Friedrichs difference scheme. The proof of compactness of approximate solutions involves Tartar commutation relations for entropy pairs. The same method is applied for the proof of compactness of bounded entropy solutions. An imbalance of regularity of different parts of Tartar relations is used. To this end, singularities are studied for fractional derivatives of weak entropies, and for the corresponding entropy fluxes. Finally, the authors investigate the large-time behavior of entropy solutions.
reviewed by: V. V. Shelukhin
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 1501926
zbMATH Keywords: conservation law
zbMATH Keywords: one-dimensional Euler equations
zbMATH Keywords: isentropic compressible fluid
zbMATH Keywords: existence of entropy solutions
zbMATH Keywords: vanishing artificial viscosity method
zbMATH Keywords: Lax-Friedrichs difference scheme
zbMATH Keywords: compactness of approximate solutions
zbMATH Keywords: Tartar commutation relations
zbMATH Keywords: compactness of bounded entropy solutions
zbMATH Keywords: singularities
MaRDI profile type: Publication
full work available at URL: s002050000091
OpenAlex ID: W2007929742
Wikidata QID: Q57386547
DOI: 10.1007/S002050000091
description: scientific article; zbMATH DE number 1501926