Global stability of solutions with discontinuous initial data containing vacuum states for the isentropic Euler equations
type: Item
instance of: scholarly article
title: Global stability of solutions with discontinuous initial data containing vacuum states for the isentropic Euler equations
zbMATH Open document ID: 1067.35059
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2004-09-22T00:00:00Z
review text: The paper deals with the global stability of entropy solutions in \(L^\infty\) containing vacuum states for the isentropic Euler equations \[ \partial_t\rho+\partial_x m=0,\qquad \partial_t m+\partial_x(m^2/\rho+p(\rho))=0, \] where \(\rho, m,\) and \(p\) represent the density, the mass, and the pressure, respectively, and are in the physical region \[ \{(\rho,m)\; : \;\rho\geq 0,\;| m/\rho| \leq C_0\} \] for some \(C_0>0.\) The uniqueness of Lipschitz solutions with discontinuous initial data is obtained in the broad class of entropy solutions in \(L^\infty\) containing vacuum states.
Mathematics Subject Classification ID: 35Q05
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 2101587
zbMATH Keywords: isotropic Euler equations
zbMATH Keywords: entropy solutions
zbMATH Keywords: continuous solutions
zbMATH Keywords: discontinuous initial data
zbMATH Keywords: global stability
zbMATH Keywords: uniqueness
author: Yachun Li
reviewed by: G. Jaiani
MaRDI profile type: Publication
full work available at URL: s00033-003-3005-8
OpenAlex ID: W2063620155
DOI: 10.1007/S00033-003-3005-8
description: scientific article; zbMATH DE number 2101587