The Riemann problem of relativistic Euler system with Synge energy
The Riemann problem of relativistic Euler system with Synge energy
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发表时间：
2020-01
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通讯作者：
T. Ruggeri;Qinghua Xiao;Huijiang Zhao
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作者：
T. Ruggeri;Qinghua Xiao;Huijiang Zhao
在本文中，我们研究了稀薄单原子和双原子气体相对论欧拉系统的黎曼问题，此时能量本构方程是唯一与相对论动力学理论兼容的Synge方程。 Synge方程涉及第二类修正贝塞尔函数，这使得相对论欧拉系统变得相当复杂。基于对第二类修正贝塞尔函数的精细估计，我们详细研究了基本双曲性质和基本波的结构，特别是激波的结构，从而严格地提供了这些相对论欧拉系统的黎曼问题的数学理论，类似于经典系统的相应理论。
In this paper, we study the Riemann problem of relativistic Euler system for rarefied monatomic and diatomic gases when the constitutive equation for the energy is the Synge equation that is the only one compatible with the relativistic kinetic theory. The Synge equation is involved with modified Bessel functions of the second kind and this makes the relativistic Euler system quite complex. Based on delicate estimates of the modified Bessel functions of the second kind, we provide a detailed investigation of basic hyperbolic properties and the structure of elementary waves, especially for the structure of shock waves and in this way, the mathematical theory of the Riemann problem for these relativistic Euler system, which is analogous to the corresponding theory of the classical ones, is rigorously provided.