Global existence and stability of a stationary Mach reflection  

作　　者：CHEN Shu Xing 

机构地区：[1]School of Mathematical Sciences, Fudan University

出　　处：《Science China Mathematics》2015年第1期11-34,共24页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11031001 and 11101101)

摘　　要：We prove the global existence and stability of a wave structure containing a stationary Mach con- figuration, which occurs when an incident shock front hits a wall with a large incident angle. Our result shows that tile data of the upstream flow and the pressure at downstream part jointly determine the whole flow, as well a the wave structure. Particularly, we show that the height of the Mach stem depends not only on the data of upstream flow, but also on the pressure at downstream flow. The flow with the assigned wave structure is governed by a free boundary value problem for the Euler system. In the problem the location of the triple point, the shock fronts and the contact discontinuity are all unknown, they are finally determined together with the solution.We prove the global existence and stability of a wave structure containing a stationary Mach configuration,which occurs when an incident shock front hits a wall with a large incident angle.Our result shows that the data of the upstream flow and the pressure at downstream part jointly determine the whole flow,as well as the wave structure.Particularly,we show that the height of the Mach stem depends not only on the data of upstream flow,but also on the pressure at downstream flow.The flow with the assigned wave structure is governed by a free boundary value problem for the Euler system.In the problem the location of the triple point,the shock fronts and the contact discontinuity are all unknown,they are finally determined together with the solution.

关 键 词：Euler system Mach reflection EXISTENCE STABILITY free boundary problem elliptic-hyperboliccomposcd system 

分 类 号：O175.21[理学—数学]