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Zero-viscosity limit of the incompressible Navier-Stokes equations with sharp vorticity gradient
Liao, Jiajiang1,2; Sueur, Franck3,4; Zhang, Ping1,2,5
2020-05-05
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume268Issue:10Pages:5855-5891
AbstractIt 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.
DOI10.1016/j.jde.2019.11.018
Indexed BySCI
Language英语
Funding ProjectAgence 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 Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000517758500008
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50838
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhang, Ping
Affiliation1.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
Recommended Citation
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.
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