STABILITY OF TRANSONIC JETS WITH STRONG RAREFACTION WAVES FOR TWO-DIMENSIONAL STEADY COMPRESSIBLE EULER SYSTEM

被引：1
|
作者：
Ding, Min [1 ]
Yuan, Hairong [2 ,3 ]
机构：
[1] Wuhan Univ Technol, Dept Math, Sch Sci, Wuhan 430070, Hubei, Peoples R China
[2] East China Normal Univ, Dept Math, Ctr PDE, Shanghai 200241, Peoples R China
[3] East China Normal Univ, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Compressible Euler equations; characteristic discontinuity; transonic; rarefaction wave; wave front tracking; interaction of waves; Glimm functional; 1-D PISTON PROBLEM; SUPERSONIC-FLOW;
D O I：
10.3934/dcds.2018125
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study supersonic flow past a convex corner which is surrounded by quiescent gas. When the pressure of the upstream supersonic flow is larger than that of the quiescent gas, there appears a strong rarefaction wave to rarefy the supersonic gas. Meanwhile, a transonic characteristic discontinuity appears to separate the supersonic flow behind the rarefaction wave from the static gas. In this paper, we employ a wave front tracking method to establish structural stability of such a flow pattern under non-smooth perturbations of the upcoming supersonic flow. It is an initial-value/free-boundary problem for the two-dimensional steady non-isentropic compressible Euler system. The main ingredients are careful analysis of wave interactions and construction of suitable Glimm functional, to overcome the difficulty that the strong rarefaction wave has a large total variation.
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页码：2911 / 2943
页数：33
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