Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle

doi:10.1016/j.jde.2018.09.036

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	Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle
	Huang, Feimin1,2 ; Kuang, Jie 2,3; Wang, Dehua 4; Xiang, Wei 5
刊名	JOURNAL OF DIFFERENTIAL EQUATIONS
	2019-03-15
卷号	266 期号:7 页码:4337-4376
关键词	Contact discontinuity Supersonic flow Free boundary Compressible Euler equation Finitely long nozzle
ISSN号	0022-0396
DOI	10.1016/j.jde.2018.09.036
英文摘要	In this paper, we study the stability of supersonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle of varying cross-sections. We formulate the problem as an initial-boundary value problem with the contact discontinuity as a free boundary. To deal with the free boundary value problem, we employ the Lagrangian transformation to straighten the contact discontinuity and then the free boundary value problem becomes a fixed boundary value problem. We develop an iteration scheme and establish some novel estimates of solutions for the first order of hyperbolic equations on a cornered domain. Finally, by using the inverse Lagrangian transformation and under the assumption that the incoming flows and the nozzle walls are smooth perturbations of the background state, we prove that the original free boundary problem admits a unique weak solution which is a small perturbation of the background state and the solution consists of two smooth supersonic flows separated by a smooth contact discontinuity. (C) 2018 Elsevier Inc. All rights reserved.
资助项目	NSFC[11801549] ; NSFC[11371349] ; NSFC[11688101] ; NSF[DMS-1312800] ; NSF[DMS-1613213] ; Research Grants Council of the HKSAR, China[CityU 21305215] ; Research Grants Council of the HKSAR, China[CityU 11332916] ; Research Grants Council of the HKSAR, China[CityU 11304817] ; Research Grants Council of the HKSAR, China[CityU 11303518]
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000456433000018
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/32287]
专题	应用数学研究所
通讯作者	Kuang, Jie
作者单位	1.Hunan Normal Univ, Coll Math & Stat, Changsha 410081, Hunan, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China 4.Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA 5.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Huang, Feimin,Kuang, Jie,Wang, Dehua,et al. Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2019,266(7):4337-4376.
APA	Huang, Feimin,Kuang, Jie,Wang, Dehua,&Xiang, Wei.(2019).Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle.JOURNAL OF DIFFERENTIAL EQUATIONS,266(7),4337-4376.
MLA	Huang, Feimin,et al."Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle".JOURNAL OF DIFFERENTIAL EQUATIONS 266.7(2019):4337-4376.