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TWO-DIMENSIONAL STEADY SUPERSONIC EXOTHERMICALLY REACTING EULER FLOW PAST LIPSCHITZ BENDING WALLS
Chen, Gui-Qiang G.1; Kuang, Jie2,3; Zhang, Yongqian2
2017
Source PublicationSIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN0036-1410
Volume49Issue:2Pages:818-873
AbstractWe are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of both the initial data and the slope of the boundary is sufficiently small. The flow is governed by an ideal polytropic gas and undergoes a one-step exothermic chemical reaction under the reaction rate function that is Lipschtiz and has a positive lower bound. The heat released by the reaction may cause the total variation of the solution to increase along the flow direction. We employ the modified wavefront tracking scheme to construct approximate solutions and develop a Glimm-type functional by incorporating the approximate strong rarefaction waves and Lipschitz bending walls to obtain the uniform bound on the total variation of the approximate solutions. Then we employ this bound to prove the convergence of the approximate solutions to a global entropy solution that contains a strong rarefaction wave generated by the Lipschitz bending wall. In addition, the asymptotic behavior of the entropy solution in the flow direction is also analyzed.
Keywordsteady supersonic reacting Euler flow rarefaction wave wavefront tracking scheme Lispchitz bending wall entropy solutions asymptotic behavior stability
DOI10.1137/16M1075089
Language英语
Funding ProjectUK EPSRC Award[EP/L015811/1] ; Royal Society-Wolfson Research Merit Award (UK). ; NSFC[11421061] ; NSFC[11031001] ; NSFC[11121101] ; Natural Science Foundation of Shanghai[15ZR1403900] ; 111 Project (China)[B08018]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000400748500005
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:5[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26050
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.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Chen, Gui-Qiang G.,Kuang, Jie,Zhang, Yongqian. TWO-DIMENSIONAL STEADY SUPERSONIC EXOTHERMICALLY REACTING EULER FLOW PAST LIPSCHITZ BENDING WALLS[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2017,49(2):818-873.
APA Chen, Gui-Qiang G.,Kuang, Jie,&Zhang, Yongqian.(2017).TWO-DIMENSIONAL STEADY SUPERSONIC EXOTHERMICALLY REACTING EULER FLOW PAST LIPSCHITZ BENDING WALLS.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,49(2),818-873.
MLA Chen, Gui-Qiang G.,et al."TWO-DIMENSIONAL STEADY SUPERSONIC EXOTHERMICALLY REACTING EULER FLOW PAST LIPSCHITZ BENDING WALLS".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 49.2(2017):818-873.
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