Nonlinear Hyperbolic Waves in Relativistic Gases of Massive Particles with Synge Energy
Nonlinear Hyperbolic Waves in Relativistic Gases of Massive Particles with Synge Energy
复制标题
具有 Synge 能量的大质量粒子相对论气体中的非线性双曲波
DOI：
10.1007/s00205-020-01590-8
复制
发表时间：
2020-11-17
影响因子：
2.5
通讯作者：
Zhao, Huijiang
中科院分区：
文献类型：
--
作者：
Ruggeri, Tommaso;Xiao, Qinghua;Zhao, Huijiang
本文研究了当能量的本构方程为单原子稀薄气体的Synge本构方程或双原子气体的Synge本构方程时，非线性波的一些基本性质和欧拉相对论系统的Riemann问题。这些本构方程是从经典到超相对论范围内唯一与大质量粒子相对论动力学理论相容的本构方程。它们涉及第二类修正的贝塞尔函数，这使得欧拉的相对论体系相当复杂。基于对贝塞尔函数的精细估计，我们证明了：(I)声速的极限是光速的1/3倍(强值意味着亚光性，也就是因果关系)，(Ii)声波的真正非线性，(Iii)朗肯-胡格尼奥特关系与热力学第二定律(通过所有Lax激波的熵增长)的兼容性，以及(Iv)Riemann初值问题的唯一可解性(如果我们包括非相对论背景下真空的可能性)。
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/root 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).