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Long time well-posedness of Prandtl system with small and analytic initial data
Zhang, Ping1,2; Zhang, Zhifei3
2016-04-01
Source PublicationJOURNAL OF FUNCTIONAL ANALYSIS
ISSN0022-1236
Volume270Issue:7Pages:2591-2615
AbstractIn this paper, we investigate the long time existence and uniqueness of small solution to d, for d = 2,3, dimensional Prandtl system with small initial data which is analytic in the horizontal variables. In particular, we prove that d dimensional Prandtl system has a unique solution with the life-span of which is greater than epsilon(-4/3). if the initial data is of size epsilon and the value on the boundary of the tangential velocity of the outflow are of size epsilon(5/3). We mention that the tool developed in [4,5] to make the analytical type estimates and the special structure of the nonlinear terms to this system play an essential role in the proof of this result. (C) 2016 Elsevier Inc. All rights reserved.
KeywordPrandtl system Littlewood-Paley theory Life-span Energy method
DOI10.1016/j.jfa.2016.01.004
Language英语
Funding ProjectNSF of China[11371347] ; NSF of China[11371039] ; NSF of China[11421101] ; Chinese Academy of Sciences ; National Center for Mathematics and Interdisciplinary Sciences ; MCM
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000372212200008
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:16[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/22276
Collection数学所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
3.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Ping,Zhang, Zhifei. Long time well-posedness of Prandtl system with small and analytic initial data[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2016,270(7):2591-2615.
APA Zhang, Ping,&Zhang, Zhifei.(2016).Long time well-posedness of Prandtl system with small and analytic initial data.JOURNAL OF FUNCTIONAL ANALYSIS,270(7),2591-2615.
MLA Zhang, Ping,et al."Long time well-posedness of Prandtl system with small and analytic initial data".JOURNAL OF FUNCTIONAL ANALYSIS 270.7(2016):2591-2615.
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