Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions
type: Item
instance of: scholarly article
title: Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions
zbMATH Open document ID: 0647.76049
DOI: 10.1016/0022-0396(87)90188-4
author: David H. Wagner
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: (Author`s summary.) This paper demonstrates the equivalence of the Euler and the Lagrangian equations of gas dynamics in one space dimension for weak solutions which are bounded and measurable in Eulerian coordinates. The precise hypotheses include all known global solutions on \({\mathbb{R}}\times {\mathbb{R}}\) \(+\). In particular, solutions containing vacuum states (zero mass density) are included. Furthermore, there is a one-to- one correspondence between the convex extensions of the two systems, and the corresponding admissibility criteria are equivalent. In the presence of a vacuum, the definition of weak solution for the Lagrangian equations must be strengthened to admit test functions which are discontinuous at the vacuum. As an application, we translate a large-data existence result of DiPerna for the Euler equations for isentropic gas dynamics into a similar theorem for the Lagrangian equations.
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4057204
zbMATH Keywords: Lagrangian equations
zbMATH Keywords: gas dynamics
zbMATH Keywords: Eulerian coordinates
zbMATH Keywords: global solutions
zbMATH Keywords: vacuum states
zbMATH Keywords: zero mass density
zbMATH Keywords: weak solution
zbMATH Keywords: isentropic gas dynamics
reviewed by: B. D. Sleeman
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90188-4
OpenAlex ID: W2046162815
cites work: The principle of virtual work and integral laws of motion
cites work: Q5801144
cites work: Convergence of the viscosity method for isentropic gas dynamics
cites work: Q5581948
cites work: Q5565773
cites work: Systems of Conservation Equations with a Convex Extension
cites work: Q3213510
cites work: Initial-boundary value problems for gas dynamics
cites work: On the vacuum state for the isentropic gas dynamics equations
cites work: Mixed problems for nonlinear conservation laws
cites work: THE SPACES $ BV$ AND QUASILINEAR EQUATIONS
description: scientific article; zbMATH DE number 4057204