Riemann boundary value problems and reflection of shock for the Chaplygin gas  

作　　者：CHEN ShuXing 1,& QU AiFang 2 1 School of Mathematical Sciences,Fudan University,Shanghai 200433,China 2 Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan 430071,China 

出　　处：《Science China Mathematics》2012年第4期671-685,共15页中国科学：数学（英文版）

基　　金：supported in part by National Natural Science Foundation of China(Grant No. 11031001);the Doctorial Foundation of National Educational Ministry (Grant No. 20090071110002);Tianyuan Fund of Mathematics (Grant No. 11126181)

摘　　要：In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp.In this paper, we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively, where one sector is a quadrant and the other one has an acute vertex angle. We prove that the Riemann boundary value problem admits a global self-similar solution, if either the initial states are close, or the smaller sector is also near a quadrant. Our result can be applied to solving the problem of shock reflection by a ramp.

关 键 词：Riemann boundary value problem reflection of shock Chaplygin gas wave interaction Eulersystem 

分 类 号：O186.12[理学—数学]