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Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge
Chen, Gui-Qiang1,2; Li, Tian-Hong3
2008-03-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume244Issue:6Pages:1521-1550
AbstractFor a supersonic Euler flow past a straight-sided wedge whose vertex angle is less than the extreme angle, there exists a shock-front emanating from the wedge vertex, and the shock-front is usually strong especially when the vertex angle of the wedge is large. In this paper, we establish the L-1 well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge whose boundary slope function has small total variation, when the total variation of the incoming flow is small. In this case, the Lipschitz wedge perturbs the flow, and the waves reflect after interacting with the strong shock-front and the wedge boundary. We first obtain the existence of solutions in BV when the incoming flow has small total variation by the wave front tracking method and then establish the L 1 stability of the solutions with respect to the incoming flows. In particular, we incorporate the nonlinear waves generated from the wedge boundary to develop a Lyapunov functional between two solutions containing strong shock-fronts, which is equivalent to the L-1 norm, and prove that the functional decreases in the flow direction. Then the L-1 stability is established, so is the uniqueness of the solutions by the wave front tracking method. Finally, the uniqueness of solutions in a broader class, the class of viscosity solutions, is also obtained. (c) 2007 Elsevier Inc. All rights reserved.
Keywordwell-posedness wave front tracking supersonic flow Euler flow wedge
DOI10.1016/j.jde.2007.09.005
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000255005700010
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/6512
Collection数学所
Corresponding AuthorChen, Gui-Qiang
Affiliation1.Northwestern Univ, Dept Math, Evanston, IL 60208 USA
2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Chen, Gui-Qiang,Li, Tian-Hong. Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2008,244(6):1521-1550.
APA Chen, Gui-Qiang,&Li, Tian-Hong.(2008).Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge.JOURNAL OF DIFFERENTIAL EQUATIONS,244(6),1521-1550.
MLA Chen, Gui-Qiang,et al."Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge".JOURNAL OF DIFFERENTIAL EQUATIONS 244.6(2008):1521-1550.
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