Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles

doi:10.1016/j.aim.2019.02.002

CSpace > 应用数学研究所

	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-Yi 5,6; Xiang, Wei 7
	2019-04-13
发表期刊	ADVANCES IN MATHEMATICS
ISSN	0001-8708
卷号	346 页码:946-1008
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.
关键词	Steady Euler flows Large vorticity Characteristic discontinuities Free boundary Existence Uniqueness
DOI	10.1016/j.aim.2019.02.002
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000461538800023
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	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.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
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.