Plane steady shock waves in Israel-Stewart fluids
type: Item
instance of: scholarly article
title: Plane steady shock waves in Israel-Stewart fluids
zbMATH Open document ID: 0728.76127
DOI: 10.1016/0003-4916(90)90393-3
author: Timothy S. Olson
author: William A. Hiscock
published in: Annals of Physics
publication date: 1990-01-01T00:00:00Z
review text: The authors study the existence of plane steady shock waves for relativistic dissipative fluids in the framework of the Israel-Stewart theory. Here shock waves are meant as continuous, single-valued, stable solutions connecting two asymptotic (in space) equilibrium states. They prove by means of algebraic computations that such solutions do not exist if the shock is sufficiently strong, i.e, if the upstream Mach number \(M^-=v(-\infty)/v_ s(-\infty)\), \(v_ s=[(\partial p/\partial \rho)_ s]^{1/2}\), is larger than some bound (or if the downstream Mach number \(M^+=v(+\infty)/v_ s(+\infty)\), is smaller than some bound). The reason is that at such bounds solutions become multiple- valued (some dynamical system degenerates), since the fluid velocity at some point in the shock becomes characteristic.
Mathematics Subject Classification ID: 76Y05
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 4204055
zbMATH Keywords: existence of plane steady shock waves
zbMATH Keywords: relativistic dissipative fluids
zbMATH Keywords: Israel-Stewart theory
zbMATH Keywords: continuous, single-valued, stable solutions
zbMATH Keywords: equilibrium states
reviewed by: Andrea Corli
MaRDI profile type: Publication
full work available at URL: 0003-4916(90)90393-3
OpenAlex ID: W2041608576
cites work: Stability and causality in dissipative relativistic fluids
cites work: Stability and causality in the Israel-Stewart energy frame theory
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cites work: Shock structure in relativistic fluid-dynamics
cites work: The profile of a steady plane shock wave
cites work: On the kinetic theory of rarefied gases
cites work: Shock structure for heat conducting and viscid fluids
cites work: Q3999241
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description: scientific article; zbMATH DE number 4204055