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Global Regularity of 2D Density Patches for Viscous Inhomogeneous Incompressible Flow with General Density: Low Regularity Case
Liao, Xian1,2,3; Zhang, Ping2,4
2019-04-01
Source PublicationCOMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
ISSN0010-3640
Volume72Issue:4Pages:835-884
AbstractThis paper presents some progress toward an open question proposed by P.-L. Lions [26] concerning the propagation of regularities of density patches for viscous inhomogeneous incompressible flow. We first establish the global-in-time well-posedness of the two-dimensional inhomogeneous incompressible Navier-Stokes system with initial density rho 0=eta(1)1 Omega(0)+eta(2)1 Omega(c)(0). Here (eta(1),eta(2)) is any pair of positive constants and Omega(0) is a bounded, simply connected W-3,W-p(R-2) domain. We then prove that for any positive time t, the density rho(t)=eta(1)1(Omega(t))+eta(2)1(Omega(t)c), with the domain Omega(t) preserving the W-3,W-p-boundary regularity. (c) 2018 Wiley Periodicals, Inc.
DOI10.1002/cpa.21782
Language英语
Funding ProjectMCM ; DFG[SFB 1060] ; Universitat Bonn ; NSF of China[11371347] ; NSF of China[11688101] ; National Center for Mathematics and Interdisciplinary Sciences
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000458660800004
PublisherWILEY
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32557
Collection数学所
Affiliation1.Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 1000190, Peoples R China
3.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 1000190, Peoples R China
4.Univ Chinese Acad, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Liao, Xian,Zhang, Ping. Global Regularity of 2D Density Patches for Viscous Inhomogeneous Incompressible Flow with General Density: Low Regularity Case[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,2019,72(4):835-884.
APA Liao, Xian,&Zhang, Ping.(2019).Global Regularity of 2D Density Patches for Viscous Inhomogeneous Incompressible Flow with General Density: Low Regularity Case.COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,72(4),835-884.
MLA Liao, Xian,et al."Global Regularity of 2D Density Patches for Viscous Inhomogeneous Incompressible Flow with General Density: Low Regularity Case".COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS 72.4(2019):835-884.
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