Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge

doi:10.1016/j.jde.2007.09.005

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	Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge
	Chen, Gui-Qiang 1,2; Li, Tian-Hong3
	2008-03-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	244 期号:6 页码:1521-1550
摘要	For 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.
关键词	well-posedness wave front tracking supersonic flow Euler flow wedge
DOI	10.1016/j.jde.2007.09.005
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000255005700010
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/6512
专题	数学所
通讯作者	Chen, Gui-Qiang
作者单位	1.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
推荐引用方式 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.