Global Existence and the Decay of Solutions to the Prandtl System with Small Analytic Data

doi:10.1007/s00205-021-01654-3

	Global Existence and the Decay of Solutions to the Prandtl System with Small Analytic Data
	Paicu, Marius 1; Zhang, Ping 2,3
刊名	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
	2021-04-12
页码	44
ISSN号	0003-9527
DOI	10.1007/s00205-021-01654-3
英文摘要	In this paper, we prove the global existence and the large time decay estimate of solutions to Prandtl system with small initial data, which is analytical in the tangential variable. The key ingredient used in the proof is to derive a sufficiently fast decay-in-time estimate of some weighted analytic energy estimate to a quantity, which consists of a linear combination of the tangential velocity with its primitive one, and which basically controls the evolution of the analytical radius to the solutions. Our result can be viewed as a global-in-time Cauchy-Kowalevsakya result for the Prandtl system with small analytical data, which in particular improves the previous result in Ignatova and Vicol (Arch Ration Mech Anal 220:809-848, 2016) concerning the almost global well-posedness of a two-dimensional Prandtl system.
资助项目	K.C.Wong Education Foundation ; Agence Nationale de la Recherche, Project IFSMACS[ANR-15-CE40-0010] ; NSF of China[11731007] ; NSF of China[11688101] ; National Center for Mathematics and Interdisciplinary Sciences
WOS研究方向	Mathematics ; Mechanics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000639380200001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58478]
专题	中国科学院数学与系统科学研究院
通讯作者	Paicu, Marius
作者单位	1.Univ Bordeaux, Inst Math Bordeaux, F-33405 Talence, France 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Paicu, Marius,Zhang, Ping. Global Existence and the Decay of Solutions to the Prandtl System with Small Analytic Data[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2021:44.
APA	Paicu, Marius,&Zhang, Ping.(2021).Global Existence and the Decay of Solutions to the Prandtl System with Small Analytic Data.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,44.
MLA	Paicu, Marius,et al."Global Existence and the Decay of Solutions to the Prandtl System with Small Analytic Data".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS (2021):44.