论文标题
带有同步能量的相对论欧拉系统的利曼问题
The Riemann problem of relativistic Euler system with Synge energy
论文作者
论文摘要
在本文中，我们研究了相对论欧拉系统的赖曼问题，用于稀有的单原子和双原子气体时，当能量的组成方程是同步方程，这是唯一与相对论动力学理论兼容的综合方程。 Synge方程与第二种修改的Bessel函数有关，这使相对论Euler系统非常复杂。基于对第二种修饰的贝塞尔功能的微妙估计，我们提供了对基本双曲线特性和基本波的结构的详细研究，尤其是对于冲击波的结构，通过这种方式，这些相关性Euler系统的Riemann问题的数学理论与相应的经典理论类似，是类似的经典理论。
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.
