KMS Of Academy of mathematics and systems sciences, CAS
| Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle | |
Huang, Feimin1 ; Kuang, Jie2,3; Wang, Dehua4; Xiang, Wei5
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| 2021-12-01 | |
| Source Publication | ANNALS OF PDE
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| ISSN | 2524-5317 |
| Volume | 7Issue:2Pages:96 |
| Abstract | 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. |
| Keyword | Transonic flow Contact discontinuity Free boundary Compressible Euler flow Finitely long nozzle |
| DOI | 10.1007/s40818-021-00113-2 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics ; Physics |
| WOS Subject | Mathematics ; Physics, Mathematical |
| WOS ID | WOS:000698680000001 |
| Publisher | SPRINGERNATURE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59294 |
| Collection | 应用数学研究所 |
| Corresponding Author | Wang, Dehua |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Innovat Acad Precis Measurement Sci & Technol, Wuhan 430071, Peoples R China 3.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, 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 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. |
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