Global solutions of the relativistic Euler equations
type: Item
instance of: scholarly article
title: Global solutions of the relativistic Euler equations
zbMATH Open document ID: 0780.76085
DOI: 10.1007/BF02096733
published in: Communications in Mathematical Physics
publication date: 1993-12-15T00:00:00Z
review text: We demonstrate the existence of solutions with shocks for the equations describing a perfect fluid in special relativity, namely, \(\text{div }T=0\), where \(T^{ij}=(p+\rho c^ 2)u^ i u^ j+p\eta^{ij}\) is the stress energy tensor for the fluid. Here, \(p\) denotes the pressure, \(u\) the 4-velocity, \(\rho\) the mass-energy density of the fluid, \(\eta^{ij}\) the flat Minkowski metric, and \(c\) the speed of light. We assume that the equation of state is given by \(p=\sigma^ 2\rho\), where \(\sigma^ 2\), the sound speed, is constant. For these equations, we construct bounded weak solutions of the initial value problem in two- dimensional Minkowski spacetime, for any initial data of finite total variation.
Mathematics Subject Classification ID: 76Y05
Mathematics Subject Classification ID: 83C55
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 464945
zbMATH Keywords: Glimm's method
zbMATH Keywords: existence
zbMATH Keywords: shocks
zbMATH Keywords: flat Minkowski metric
zbMATH Keywords: bounded weak solutions
zbMATH Keywords: initial value problem
author: Joel Smoller
author: Blake Temple
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 464945