KMS Of Academy of mathematics and systems sciences, CAS
| 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
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| 2019-03-15 | |
| Source Publication | JOURNAL OF DIFFERENTIAL EQUATIONS
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| ISSN | 0022-0396 |
| Volume | 266Issue:7Pages:4337-4376 |
| Abstract | 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. |
| Keyword | Contact discontinuity Supersonic flow Free boundary Compressible Euler equation Finitely long nozzle |
| DOI | 10.1016/j.jde.2018.09.036 |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000456433000018 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/32288 |
| Collection | 应用数学研究所 |
| Corresponding Author | Kuang, Jie |
| Affiliation | 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 |
| 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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