Zero-viscosity limit of the incompressible Navier-Stokes equations with sharp vorticity gradient

doi:10.1016/j.jde.2019.11.018

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	Zero-viscosity limit of the incompressible Navier-Stokes equations with sharp vorticity gradient
	Liao, Jiajiang 1,2; Sueur, Franck 3,4; Zhang, Ping 1,2,5
	2020-05-05
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	268 期号:10 页码:5855-5891
摘要	It is well-known that the 3D incompressible Euler equations admit some local-in-time solutions for which the vorticity is piecewise smooth and discontinuous across a smooth time-dependent hypersurface which evolves with the flow. In this paper we prove that such a solution can be obtained as zero-viscosity limit of strong solutions to the Navier-Stokes equations whose vorticity has sharp variations near the hypersurface associated with the inviscid limit. Indeed we exhibit some sequences of exact solutions to the Navier-Stokes equations with vanishing viscosity which are given by multi-scale asymptotic expansions involving some characteristic boundary layers given by some linear PDEs. The convergence and the validity of the expansion are guaranteed on the time interval associated with the solution to the Euler equations. (C) 2019 Elsevier Inc. All rights reserved.
DOI	10.1016/j.jde.2019.11.018
收录类别	SCI
语种	英语
资助项目	Agence Nationale de la Recherche[ANR-15-CE40-0010] ; Agence Nationale de la Recherche[ANR-16-CE40-0027-01] ; Agence Nationale de la Recherche[ANR-18-CE40-0027-01] ; NSF of China[11371347] ; NSF of China[11688101] ; Morningside Center of Mathematics of The Chinese Academy of Sciences ; National Center for Mathematics and Interdisciplinary Sciences
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000517758500008
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/50838
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Ping
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Bordeaux, Inst Math Bordeaux, F-33405 Talence, France 4.Inst Univ France, Paris, France 5.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liao, Jiajiang,Sueur, Franck,Zhang, Ping. Zero-viscosity limit of the incompressible Navier-Stokes equations with sharp vorticity gradient[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2020,268(10):5855-5891.
APA	Liao, Jiajiang,Sueur, Franck,&Zhang, Ping.(2020).Zero-viscosity limit of the incompressible Navier-Stokes equations with sharp vorticity gradient.JOURNAL OF DIFFERENTIAL EQUATIONS,268(10),5855-5891.
MLA	Liao, Jiajiang,et al."Zero-viscosity limit of the incompressible Navier-Stokes equations with sharp vorticity gradient".JOURNAL OF DIFFERENTIAL EQUATIONS 268.10(2020):5855-5891.