KMS Of Academy of mathematics and systems sciences, CAS
| Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles | |
Chen, Gui-Qiang G.1,2,3,4; Huang, Fei-Min3,4 ; Wang, Tian-Yi5,6; Xiang, Wei7
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| 2019-04-13 | |
| Source Publication | ADVANCES IN MATHEMATICS
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| ISSN | 0001-8708 |
| Volume | 346Pages:946-1008 |
| Abstract | We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles. We first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity, or the Bernoulli and entropy functions, at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets/entropy waves by nonlinear arguments. This is the first result on the global existence of solutions of the multidimensional steady compressible full Euler equations with free boundaries, which are not necessarily small perturbations of piecewise constant background solutions. The subsonic-sonic limit of the solutions is also shown. Finally, through the incompressible limit, we establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets. The methods and techniques developed here will be useful for solving other problems involving similar difficulties. (C) 2019 Elsevier Inc. All rights reserved. |
| Keyword | Steady Euler flows Large vorticity Characteristic discontinuities Free boundary Existence Uniqueness |
| DOI | 10.1016/j.aim.2019.02.002 |
| Language | 英语 |
| Funding Project | UK Engineering and Physical Sciences Research Council[EP/E035027/1] ; UK Engineering and Physical Sciences Research Council[EP/L015811/1] ; Royal Society-Wolfson Research Merit Award (UK) ; NSFC[11688101] ; NSFC[11601401] ; CAS ; Fundamental Research Funds for the Central Universities[WUT: 2017 IVA 072] ; Fundamental Research Funds for the Central Universities[WUT: 2017 IVB 066] ; CityU Start-Up Grant for New Faculty[7200429(MA)] ; Research Grants Council of the HKSAR ; University Grants Committee, China[CityU 21305215] ; University Grants Committee, China[CityU 11332916] ; University Grants Committee, China[CityU 11304817] ; University Grants Committee, China[CityU 11303518] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000461538800023 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/33372 |
| Collection | 应用数学研究所 |
| Corresponding Author | Chen, Gui-Qiang G.; Huang, Fei-Min; Wang, Tian-Yi; Xiang, Wei |
| Affiliation | 1.Univ Oxford, Math Inst, Oxford OX2 6GG, England 2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 5.Wuhan Univ Technol, Sch Sci, Dept Math, Wuhan 430070, Hubei, Peoples R China 6.Gran Sasso Sci Inst, Viale Francesco Crispi 7, I-67100 Laquila, Italy 7.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China |
| Recommended Citation GB/T 7714 | Chen, Gui-Qiang G.,Huang, Fei-Min,Wang, Tian-Yi,et al. Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles[J]. ADVANCES IN MATHEMATICS,2019,346:946-1008. |
| APA | Chen, Gui-Qiang G.,Huang, Fei-Min,Wang, Tian-Yi,&Xiang, Wei.(2019).Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles.ADVANCES IN MATHEMATICS,346,946-1008. |
| MLA | Chen, Gui-Qiang G.,et al."Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles".ADVANCES IN MATHEMATICS 346(2019):946-1008. |
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