STABILITY OF CONICAL SHOCKS IN THE THREE-DIMENSIONAL STEADY SUPERSONIC ISOTHERMAL FLOWS PAST LIPSCHITZ PERTURBED CONES

doi:10.1137/20M1357962

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	STABILITY OF CONICAL SHOCKS IN THE THREE-DIMENSIONAL STEADY SUPERSONIC ISOTHERMAL FLOWS PAST LIPSCHITZ PERTURBED CONES
	Chen, Gui-Qiang G.1,2,3; Kuang, Jie 2,4,5; Zhang, Yongqian 2
	2021
发表期刊	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN	0036-1410
卷号	53 期号:3 页码:2811-2862
摘要	We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are governed by the steady isothermal Euler equations for potential flow with axisymmetry so that the equations contain a singular geometric source term. We first formulate the shock stability problem as an initial boundary value problem with the leading conical shock-front as a free boundary, and then establish the existence and structural/asymptotic stability of global entropy solutions of bounded variation (BV) of the problem. To achieve this, we first develop a modified Glimm scheme to construct approximate solutions via self-similar solutions as building blocks in order to incorporate with the geometric source term. Then we introduce the Glimm-type functional, based on the local interaction estimates between weak waves, the strong leading conical shock, and self-similar solutions, as well as the estimates of the center changes of the self-similar solutions. To make sure of the decrease of the Glimm-type functional, we choose appropriate weights by careful asymptotic analysis of the reflection coefficients in the interaction estimates, when the Mach number of the incoming flow is sufficiently large. Finally, we establish the existence of global entropy solutions involving a strong leading conical shock-front, besides weak waves, under the conditions that the Mach number of the incoming flow is sufficiently large and the weighted total variation of the slopes of the generating curve of the Lipschitz perturbed cone is sufficiently small. Furthermore, the entropy solution is shown to approach asymptotically the self-similar solution that is determined by the incoming flow and the asymptotic tangent of the cone boundary at infinity.
关键词	conical shocks structural stability steady flow supersonic isothermal flow perturbed cones Lipschitz cones entropy solutions BV modified Glimm scheme TV Glimm-type functional self-similar solutions interaction estimates reflection coefficients free boundary asymptotic behavior
DOI	10.1137/20M1357962
收录类别	SCI
语种	英语
资助项目	UK Engineering and Physical Sciences Research Council (EPSRC)[EP/L015811/1] ; Royal Society-Wolfson Research Merit Award (UK) ; NSFC[11801549] ; NSFC[11971024] ; NSFC[11421061] ; NSFC[11031001] ; NSFC[11121101] ; Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences[Y8S001104] ; 111 Project (China)[B08018] ; Shanghai Natural Science Foundation[15ZR1403900]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000674276100005
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59009
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Gui-Qiang G.
作者单位	1.Univ Oxford, Math Inst, Oxford OX2 6GG, England 2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Innovat Acad Precis Measurement Sci & Technol, Wuhan 430071, Peoples R China 5.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China
推荐引用方式 GB/T 7714	Chen, Gui-Qiang G.,Kuang, Jie,Zhang, Yongqian. STABILITY OF CONICAL SHOCKS IN THE THREE-DIMENSIONAL STEADY SUPERSONIC ISOTHERMAL FLOWS PAST LIPSCHITZ PERTURBED CONES[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2021,53(3):2811-2862.
APA	Chen, Gui-Qiang G.,Kuang, Jie,&Zhang, Yongqian.(2021).STABILITY OF CONICAL SHOCKS IN THE THREE-DIMENSIONAL STEADY SUPERSONIC ISOTHERMAL FLOWS PAST LIPSCHITZ PERTURBED CONES.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,53(3),2811-2862.
MLA	Chen, Gui-Qiang G.,et al."STABILITY OF CONICAL SHOCKS IN THE THREE-DIMENSIONAL STEADY SUPERSONIC ISOTHERMAL FLOWS PAST LIPSCHITZ PERTURBED CONES".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 53.3(2021):2811-2862.