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Incompressible limit of solutions of multidimensional steady compressible Euler equations
Chen, Gui-Qiang G.1,2,3; Huang, Feimin1; Wang, Tian-Yi1,3,4,5,6; Xiang, Wei1,7
2016-06-01
Source PublicationZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
ISSN0044-2275
Volume67Issue:3Pages:18
AbstractA compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass conservation and the vorticity. Another observation is that the incompressibility of the limit for the homentropic Euler flow is directly from the continuity equation, while the incompressibility of the limit for the full Euler flow is from a combination of all the Euler equations. As direct applications of the compactness framework, we establish two incompressible limit theorems for multidimensional steady Euler flows through infinitely long nozzles, which lead to two new existence theorems for the corresponding problems for multidimensional steady incompressible Euler equations.
KeywordMultidimensional Incompressible limit Steady flow Euler equations Compressible flow Full Euler flow Homentropic flow Compactness framework Strong convergence
DOI10.1007/s00033-016-0629-z
Language英语
Funding ProjectUK EPSRC Science and Innovation Award[EP/E035027/1] ; UK EPSRC Award[EP/L015811/1] ; Royal Society-Wolfson Research Merit Award ; National Center for Mathematics and Interdisciplinary Sciences ; AMSS ; CAS ; NSFC[11371349] ; NSFC[11371064] ; China Scholarship Council[201204910256] ; CityU Start-Up Grant for New Faculty[7200429] ; Hong Kong under GRF/ECS Grant[9048045 (CityU 21305215)]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000378940400041
PublisherSPRINGER BASEL AG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/23081
Collection应用数学研究所
Corresponding AuthorChen, Gui-Qiang G.
Affiliation1.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
3.Univ Oxford, Math Inst, Radcliffe Observ Quarter, Woodstock Rd, Oxford OX2 6GG, England
4.Wuhan Univ Technol, Dept Math, Sch Sci, Wuhan 430070, Hubei, Peoples R China
5.Gran Sasso Sci Inst, Viale Francesco Crispi 7, I-67100 Laquila, Italy
6.Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China
7.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Chen, Gui-Qiang G.,Huang, Feimin,Wang, Tian-Yi,et al. Incompressible limit of solutions of multidimensional steady compressible Euler equations[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,2016,67(3):18.
APA Chen, Gui-Qiang G.,Huang, Feimin,Wang, Tian-Yi,&Xiang, Wei.(2016).Incompressible limit of solutions of multidimensional steady compressible Euler equations.ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,67(3),18.
MLA Chen, Gui-Qiang G.,et al."Incompressible limit of solutions of multidimensional steady compressible Euler equations".ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 67.3(2016):18.
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