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Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations
Chen, Gui-Qiang G.1,2,3; Chen, Jun4; Feldman, Mikhail5
2017
Source PublicationINTERFACES AND FREE BOUNDARIES
ISSN1463-9963
Volume19Issue:4Pages:591-626
AbstractThe existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong transonic shocks under the perturbation of the upstream supersonic flow and the wedge boundary is proved. The problem is formulated as a one-phase free boundary problem, in which the transonic shock is treated as a free boundary. The full Euler equations are decomposed into two algebraic equations and a first-order elliptic system of two equations in Lagrangian coordinates. With careful elliptic estimates by using appropriate weighted Holder norms, the iteration map is defined and analyzed, and the existence of its fixed point is established by performing the Schauder fixed point argument. The careful analysis of the asymptotic behavior of the solutions reveals particular characters of the full Euler equations.
KeywordShock wave free boundary wedge problem steady supersonic subsonic transonic mixed type composite type hyperbolic-elliptic full Euler equations physical admissible existence stability asymptotic behavior decay rate
DOI10.4171/IFB/394
Language英语
Funding ProjectUK Engineering and Physical Sciences Research Council Award[EP/L015811/1] ; Royal Society-Wolfson Research Merit Award (UK) ; Sustech Start-up Grant[Y01286205] ; National Science Foundation[DMS-1401490] ; Van Vleck Professorship Research - University of Wisconsin-Madison
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000422714700005
PublisherEUROPEAN MATHEMATICAL SOC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29315
Collection中国科学院数学与系统科学研究院
Affiliation1.Univ Oxford, Math Inst, Oxford OX2 6GG, England
2.Chinese Acad Sci, AMSS, Beijing 100190, Peoples R China
3.Chinese Acad Sci, UCAS, Beijing 100190, Peoples R China
4.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
5.Univ Wisconsin, Dept Math, Madison, WI 53706 USA
Recommended Citation
GB/T 7714
Chen, Gui-Qiang G.,Chen, Jun,Feldman, Mikhail. Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations[J]. INTERFACES AND FREE BOUNDARIES,2017,19(4):591-626.
APA Chen, Gui-Qiang G.,Chen, Jun,&Feldman, Mikhail.(2017).Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations.INTERFACES AND FREE BOUNDARIES,19(4),591-626.
MLA Chen, Gui-Qiang G.,et al."Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations".INTERFACES AND FREE BOUNDARIES 19.4(2017):591-626.
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