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Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle
Huang, Feimin1,2; Kuang, Jie2,3; Wang, Dehua4; Xiang, Wei5
2019-03-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume266Issue:7Pages:4337-4376
AbstractIn 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.
KeywordContact discontinuity Supersonic flow Free boundary Compressible Euler equation Finitely long nozzle
DOI10.1016/j.jde.2018.09.036
Language英语
Funding ProjectNSFC[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 Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000456433000018
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32288
Collection应用数学研究所
Affiliation1.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
Recommended Citation
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.
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