Journal ArticleDOI
Nonlinear Hyperbolic Waves in Relativistic Gases of Massive Particles with Synge Energy
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In this article, the authors studied fundamental properties of nonlinear waves and the Riemann problem of Euler's relativistic system when the constitutive equation for energy is that of Synge for a monatomic rarefied gas or its generalization for diatomic gas.Abstract:
In this article, we study some fundamental properties of nonlinear waves and the Riemann problem of Euler’s relativistic system when the constitutive equation for energy is that of Synge for a monatomic rarefied gas or its generalization for diatomic gas. These constitutive equations are the only ones compatible with the relativistic kinetic theory for massive particles in the whole range from the classical to the ultra-relativistic regime. They involve modified Bessel functions of the second kind and this makes Euler’s relativistic system rather complex. Based on delicate estimates of the Bessel functions, we prove: (i) a limit on the speed of sound of $$1{/}\sqrt{3}$$
times the speed of light (which a fortiori implies subluminality, that is causality), (ii) the genuine non-linearity of the acoustic waves, (iii) the compatibility of Rankine–Hugoniot relations with the second law of thermodynamics (entropy growth through all Lax shocks), and (iv) the unique resolvability of the initial value problem of Riemann (if we include the possibility of vacuum as in the non-relativistic context).read more
Citations
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On relativistic gasdynamics: invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections
TL;DR: In this paper, a classical system of conservation laws descriptive of relativistic gasdynamics is examined, and the system is shown to be invariant under a novel multi-parameter model.
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Maxwellian iteration of a causal relativistic model of polyatomic gases and evaluation of bulk, shear viscosity and heat conductivity
TL;DR: In this article, the parabolic limit of the field equations of a recent hyperbolic model of relativistic polyatomic gas in the framework of Rational Extended Thermodynamics (RET) theory is given.
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On a relativistic BGK model for polyatomic gases near equilibrium
TL;DR: In this paper, the authors prove the unique existence and asymptotic behavior of classical solutions to the relativistic polyatomic BGK model when the initial data is sufficiently close to a global equilibrium.
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Formation of vacuum state and delta shock wave for the relativistic Euler system for polytropic gas with the varying $$\gamma $$-law
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On a Relativistic BGK Model for Polyatomic Gases Near Equilibrium
TL;DR: In this article , the authors prove the unique existence and asymptotic behavior of classical solutions to the relativistic polyatomic BGK model when the initial data is sufficiently close to a global equilibrium.
References
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