Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations

doi:10.4171/IFB/394

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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, Jun 4; Feldman, Mikhail 5
	2017
发表期刊	INTERFACES AND FREE BOUNDARIES
ISSN	1463-9963
卷号	19 期号:4 页码:591-626
摘要	The 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.
关键词	Shock 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
DOI	10.4171/IFB/394
语种	英语
资助项目	UK 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研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000422714700005
出版者	EUROPEAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29315
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Gui-Qiang G.
作者单位	1.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
推荐引用方式 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.