Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles
文献类型：期刊论文
| 作者 | Chen, Gui-Qiang G.1,4,5,6; Huang, Fei-Min4,5 ; Wang, Tian-Yi2,3; Xiang, Wei7
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| 刊名 | ADVANCES IN MATHEMATICS
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| 出版日期 | 2019-04-13 |
| 卷号 | 346页码:946-1008 |
| 关键词 | Steady Euler flows Large vorticity Characteristic discontinuities Free boundary Existence Uniqueness |
| ISSN号 | 0001-8708 |
| DOI | 10.1016/j.aim.2019.02.002 |
| 英文摘要 | 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. |
| 资助项目 | 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研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000461538800023 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/33372]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Chen, Gui-Qiang G.; Huang, Fei-Min; Wang, Tian-Yi; Xiang, Wei |
| 作者单位 | 1.Univ Oxford, Math Inst, Oxford OX2 6GG, England 2.Gran Sasso Sci Inst, Viale Francesco Crispi 7, I-67100 Laquila, Italy 3.Wuhan Univ Technol, Sch Sci, Dept Math, Wuhan 430070, Hubei, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 6.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 7.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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