CSpace
Striated Regularity of 2-D Inhomogeneous Incompressible Navier-Stokes System with Variable Viscosity
Paicu, Marius1; Zhang, Ping2,3,4
2020-05-01
Source PublicationCOMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN0010-3616
Volume376Issue:1Pages:385-439
AbstractIn this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous across some smooth interface. Compared with the previous results for the inhomogeneous Navier-Stokes equations with constant viscosity, the main difficulty here lies in the fact that the L1 in time Lipschitz estimate of the velocity field can not be obtained by energy method (see Danchin and Mucha in The incompressible Navier-Stokes equations in vacuum; Liao and Zhang in Arch Ration Mech Anal 220:937-981, 2016; Commun Pure Appl Math 72:835-884, 2019 for instance). Motivated by the key idea of Chemin to solve 2-D vortex patch of ideal fluid (Chemin in Invent Math 103:599-629, 1991; Ann Sci ecole Norm Sup 26(4):517-542, 1993), namely, striated regularity can help to get the L infinity boundedness of the double Riesz transform, we derive the a prioriL1 in time Lipschitz estimate of the velocity field under the assumption that the viscous coefficient is close enough to a positive constant in the bounded function space. As an application, we shall prove the propagation of H52 regularity of the interface between fluids with different densities and viscosities.
DOI10.1007/s00220-019-03446-z
Indexed BySCI
Language英语
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000530733400011
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51458
Collection中国科学院数学与系统科学研究院
Corresponding AuthorPaicu, Marius
Affiliation1.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
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Paicu, Marius,Zhang, Ping. Striated Regularity of 2-D Inhomogeneous Incompressible Navier-Stokes System with Variable Viscosity[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2020,376(1):385-439.
APA Paicu, Marius,&Zhang, Ping.(2020).Striated Regularity of 2-D Inhomogeneous Incompressible Navier-Stokes System with Variable Viscosity.COMMUNICATIONS IN MATHEMATICAL PHYSICS,376(1),385-439.
MLA Paicu, Marius,et al."Striated Regularity of 2-D Inhomogeneous Incompressible Navier-Stokes System with Variable Viscosity".COMMUNICATIONS IN MATHEMATICAL PHYSICS 376.1(2020):385-439.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Paicu, Marius]'s Articles
[Zhang, Ping]'s Articles
Baidu academic
Similar articles in Baidu academic
[Paicu, Marius]'s Articles
[Zhang, Ping]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Paicu, Marius]'s Articles
[Zhang, Ping]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.