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 Stability of transonic shocks in steady supersonic flow past multidimensional wedges Chen, Gui-Qiang1,4,5; Fang, Beixiang2,3 2017-07-09 Source Publication ADVANCES IN MATHEMATICS ISSN 0001-8708 Volume 314Pages:493-539 Abstract 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. Keyword 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 Language 英语 Funding Project 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 Research Area Mathematics WOS Subject Mathematics WOS ID WOS:000403741500013 Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/25893 Collection 中国科学院数学与系统科学研究院 Corresponding Author Chen, Gui-Qiang Affiliation 1.Univ Oxford, Math Inst, Oxford OX2 6GG, England2.Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China3.Shanghai Jiao Tong Univ, MOE LSC, Shanghai 200240, Peoples R China4.Chinese Acad Sci, AMSS, Beijing 100190, Peoples R China5.Chinese Acad Sci, UCAS, Beijing 100190, Peoples R China Recommended CitationGB/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.
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