物理
黎曼问题
查普利金天然气
跨音速
简并能级
黎曼假设
冲击波
数学分析
边值问题
测速仪
特征向量
多变过程
数学
经典力学
机械
量子力学
空气动力学
暗能量
宇宙学
作者
Lihui Guo,Wancheng Sheng,Tong Zhang
出处
期刊:Communications on Pure and Applied Analysis
[American Institute of Mathematical Sciences]
日期:2010-01-01
卷期号:9 (2): 431-458
被引量:106
标识
DOI:10.3934/cpaa.2010.9.431
摘要
The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system consists of interactions of four planar elementary waves. Different from polytropic gas, all of them are contact discontinuities due to the system is full linear degenerate, i.e., the three eigenvalues of the system are linear degenerate. They include compressive one ($S^\pm$), rarefactive one ($R^\pm$) and slip lines ($J^\pm$). We still call $S^\pm$ as shock and $R^\pm$ as rarefaction wave. In this paper, we study the problem systematically. According to different combination of four elementary waves, we deliver a complete classification to the problem. It contains 14 cases in all. The Riemann solutions are self-similar, and the flow is transonic in self-similar plane $(x/t,y/t)$. The boundaries of the interaction domains are obtained. Solutions in supersonic domains are constructed in no $J$ cases. While in the rest cases, the structure of solutions are conjectured except for the case $2J^++2J^-$. Especially, delta waves and simple waves appear in some cases. The Dirichlet boundary value problems in subsonic domains or the boundary value problems for transonic flow are formed case by case. The domains are convex for two cases, and non-convex for the rest cases. The boundaries of the domains are composed of sonic curves and/or slip lines.
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