Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle

doi:10.1007/s40818-021-00113-2

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	Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle
	Huang, Feimin 1; Kuang, Jie 4,5; Wang, Dehua 3; Xiang, Wei 2
刊名	ANNALS OF PDE
	2021-12-01
卷号	7 期号:2 页码:96
关键词	Transonic flow Contact discontinuity Free boundary Compressible Euler flow Finitely long nozzle
ISSN号	2524-5317
DOI	10.1007/s40818-021-00113-2
英文摘要	We consider the stability of transonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle. This is the first work on the mixed-type problem of transonic flows across a contact discontinuity as a free boundary in nozzles. We start with the Euler-Lagrangian transformation to straighten the contact discontinuity in the new coordinates. However, the upper nozzle wall in the subsonic region depending on the mass flux becomes a free boundary after the transformation. Then we develop new ideas and techniques to solve the free-boundary problem in three steps: (1) we fix the free boundary and generate a new iteration scheme to solve the corresponding fixed boundary value problem of the hyperbolic-elliptic mixed type by building some powerful estimates for both the first-order hyperbolic equation and a second-order nonlinear elliptic equation in a Lipschitz domain; (2) we update the new free boundary by constructing a mapping that has a fixed point; (3) we establish via the inverse Lagrangian coordinate transformation that the original free interface problem admits a unique piecewise smooth transonic solution near the background state, which consists of a smooth subsonic flow and a smooth supersonic flow with a contact discontinuity.
资助项目	National Center for Mathematics and Interdisciplinary Sciences ; AMSS ; CAS ; NSFC[11371349] ; NSFC[11688101] ; NSFC[11801549] ; NSFC[11971024] ; Start-Up Research Grant from Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences[Y8S001104] ; Research Grants Council of the HKSAR, China[CityU 11304817] ; Research Grants Council of the HKSAR, China[CityU 11303518] ; Research Grants Council of the HKSAR, China[CityU 11304820] ; Research Grants Council of the HKSAR, China[CityU 11300021] ; NSF[DMS-1907519] ; NSF[1613213]
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	SPRINGERNATURE
WOS记录号	WOS:000698680000001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59293]
专题	应用数学研究所
通讯作者	Wang, Dehua
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 2.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China 3.Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA 4.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China 5.Chinese Acad Sci, Innovat Acad Precis Measurement Sci & Technol, Wuhan 430071, Peoples R China
推荐引用方式 GB/T 7714	Huang, Feimin,Kuang, Jie,Wang, Dehua,et al. Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle[J]. ANNALS OF PDE,2021,7(2):96.
APA	Huang, Feimin,Kuang, Jie,Wang, Dehua,&Xiang, Wei.(2021).Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle.ANNALS OF PDE,7(2),96.
MLA	Huang, Feimin,et al."Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle".ANNALS OF PDE 7.2(2021):96.