Stability of transonic shocks in steady supersonic flow past multidimensional wedges

doi:10.1016/j.aim.2017.04.019

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	Stability of transonic shocks in steady supersonic flow past multidimensional wedges
	Chen, Gui-Qiang 1,4,5; Fang, Beixiang 2,3
	2017-07-09
发表期刊	ADVANCES IN MATHEMATICS
ISSN	0001-8708
卷号	314 页码:493-539
摘要	We are concerned with the stability of multidimensional (M-D) transonic shocks in steady supersonic flow past multidimensional wedges. One of our motivations is that the global stability issue for the M-D case is much more sensitive than that for the 2-D case, which requires more careful rigorous mathematical analysis. In this paper, we develop a nonlinear approach and employ it to establish the stability of weak shock solutions containing a transonic shock front for potential flow with respect to the M-D perturbation of the wedge boundary in appropriate function spaces. To achieve this, we first formulate the stability problem as a free boundary problem for nonlinear elliptic equations. Then we introduce the partial hodograph transformation to reduce the free boundary problem into a fixed boundary value problem near a background solution with fully nonlinear boundary conditions for second-order nonlinear elliptic equations in an unbounded domain. To solve this reduced problem, we linearize the nonlinear problem on the background shock solution and then, after solving this linearized elliptic problem, develop a nonlinear iteration scheme that is proved to be contractive. (C) 2017 Elsevier Inc. All rights reserved.
关键词	Stability Multidimensional M-D Transonic shocks Steady Supersonic Wedge Nonlinear approach Iteration scheme A priori estimates Boundary value problems Weighted norms Instability Asymptotic behavior
DOI	10.1016/j.aim.2017.04.019
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] ; NSFC[10728101] ; Royal Society - Wolfson Research Merit Award (UK) ; Natural Science Foundation of China[11031001] ; Natural Science Foundation of China[11371250] ; Natural Science Foundation of China[11631008] ; Shanghai Committee of Science and Technology[15XD1502300] ; Shanghai Jiao Tong University ; University of Oxford ; State Scholarship Fund of China Scholarship Council[2011831005] ; Shanghai Jiao Tong University's Chenxing SMC-B Project
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000403741500013
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/25893
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Gui-Qiang
作者单位	1.Univ Oxford, Math Inst, Oxford OX2 6GG, England 2.Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China 3.Shanghai Jiao Tong Univ, MOE LSC, Shanghai 200240, Peoples R China 4.Chinese Acad Sci, AMSS, Beijing 100190, Peoples R China 5.Chinese Acad Sci, UCAS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Chen, Gui-Qiang,Fang, Beixiang. Stability of transonic shocks in steady supersonic flow past multidimensional wedges[J]. ADVANCES IN MATHEMATICS,2017,314:493-539.
APA	Chen, Gui-Qiang,&Fang, Beixiang.(2017).Stability of transonic shocks in steady supersonic flow past multidimensional wedges.ADVANCES IN MATHEMATICS,314,493-539.
MLA	Chen, Gui-Qiang,et al."Stability of transonic shocks in steady supersonic flow past multidimensional wedges".ADVANCES IN MATHEMATICS 314(2017):493-539.