具有球对称结构的相对论欧拉方程组稳态解的存在性

数学物理学报 ›› 2014, Vol. 34 ›› Issue (4): 841-850.

具有球对称结构的相对论欧拉方程组稳态解的存在性

耿永才

上海应用技术学学院理学院上海 200235

收稿日期:2013-02-21 修回日期:2014-03-15 出版日期:2014-08-25 发布日期:2014-08-25
基金资助:
国家自然科学基金(11201308)、上海市优青项目(ZZyyy12025)和上海市创新项目(13ZZ136)资助

Steady State Solutions of Relativistic Euler Equations with Spherical Symmetry

GENG Yong-Cai

School of Science, Shanghai Institute of Technology, Shanghai 200235

Received:2013-02-21 Revised:2014-03-15 Online:2014-08-25 Published:2014-08-25
Supported by:
国家自然科学基金(11201308)、上海市优青项目(ZZyyy12025)和上海市创新项目(13ZZ136)资助

摘要/Abstract

摘要：

对于等温气体, 作者将考虑具有球对称结构的相对论欧拉方程组经典稳态解(定理1.1)和弱稳态解(定理1.2)的存在性. 通过求解两个常微分方程以及比较马赫数M和1的关系, 定理1.1证明了相对论欧拉方程组经典稳态解的存在性. 在一个C^2, ^α, α∈(0,1)稳态背景解的扰动下, 定理1.2将证明高维球对称跨音速(双曲-椭圆)解的存在性.

关键词: 相对论欧拉方程组, 球对称, 稳态解

Abstract:

In this paper, for isothermal gas, we will think about the existence of classical (Theorem 1.1) and weak (Theorem 1.2) solutions of steady state relativistic Euler equations with spherical symmetry structure, respectively. Theorem 1.1 shows that, by solving two ordinary differential equations and according to the comparison of Mach number M and 1, we establish the existence of classical solutions. Moreover, Theorem 1.2 shows that, under a C^2, ^α, α∈(0,1) steady perturbation of the upstream supersonic flow, we will prove the existence of steady multidimensional transonic shocks (hyperbolic-elliptic shocks) for spherically symmetric relativistic Euler equations.

Key words: Relativistic Euler equations, Spherical symmetry, Steady state solutions

中图分类号:

60F15

耿永才. 具有球对称结构的相对论欧拉方程组稳态解的存在性[J]. 数学物理学报, 2014, 34(4): 841-850.

GENG Yong-Cai. Steady State Solutions of Relativistic Euler Equations with Spherical Symmetry[J]. Acta mathematica scientia,Series A, 2014, 34(4): 841-850.

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