Conservation laws for relativistic fluid dynamics
type: Item
instance of: scholarly article
title: Conservation laws for relativistic fluid dynamics
zbMATH Open document ID: 0909.76108
author: Jing Chen
published in: Archive for Rational Mechanics and Analysis
publication date: 1997-12-10T00:00:00Z
review text: This paper presents a rigorous mathematical theory of relativistic fluid dynamics using equations developed by \textit{A. H. Taub} [Annu. Rev. Fluid Mech. 10, 301--332 (1978; Zbl 0403.76097)]. Despite the complexity of the system, a complete analogy is established between classical and relativistic hydrodynamics. In particular, it is shown that the Newtonian limits of these results reduce to the classical results. To exclude the formation of a vacuum, the condition \(R_L> S_R\) is introduced, where \(R\) and \(S\) are Riemann invariants, \(R_L\) is the value of \(R\) at \(x\leq 0\), and \(S_R\) is the value of \(S\) at \(x>0\). The \((p,\nu)\)-plane is used in the analysis, and it is shown that it leads to the unique determination of the solution of the Riemann problem.
Mathematics Subject Classification ID: 76Y05
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1096005
zbMATH Keywords: analogy between classical and relativistic hydrodynamics
zbMATH Keywords: Newtonian limits
zbMATH Keywords: Riemann invariants
zbMATH Keywords: Riemann problem
reviewed by: Alan Jeffrey
MaRDI profile type: Publication
full work available at URL: s002050050057
OpenAlex ID: W2014304209
DOI: 10.1007/S002050050057
description: scientific article; zbMATH DE number 1096005