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On the global well-posedness of 2-D inhomogeneous incompressible Nayier Stokes system with variable viscous coefficient
Abidi, Hammadi1; Zhang, Ping2,3
2015-10-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume259Issue:8Pages:3755-3802
AbstractGiven solenoidal vector u(0) is an element of(H) over dot(-2 delta) boolean AND H-1 (R-2), rho(0) - l is an element of L-2(R-2), and rho 0 L-infinity boolean AND (W) over bar (1,r)(R-2), with a positive lower bound for delta is an element of(0, 1/2) and 2 < r < 2/1-2 delta, we prove that 2-D incompressible inhomogeneous Navier-Stokes system (1.1) has a unique global solution provided that the viscous coefficient mu(rho(0)) is close enough to 1 in the L-infinity norm compared to the size of A and the norms of the initial data. With smoother initial data, we can prove the propagation of regularities for such solutions. Furthermore, for 1 < p < 4, if (rho(0) - 1, u(0)) belongs to the critical Besov spaces (B) over bar (2/p)(p,1)(R-2) x ((B) over bar (-1+2/p)(p,1) boolean AND L-2(R-2)) and the (B) over bar (2/p)(p,1) (R-2) norm of rho(0) - 1 is sufficiently small compared to the exponential of parallel to u(0)parallel to(2)(L2) + parallel to u(0)parallel to((B) over barp,1-1+2/p), we prove the global well-posedness of (1.1) in the scaling invariant spaces. Finally for initial data in the almost critical Besov spaces, we prove the global well-posedness of (1.1) under the assumption that the L-infinity norm of rho(0) - 1 is sufficiently small. (C) 2015 Elsevier Inc. All rights reserved.
KeywordInhomogeneous Navier-Stokes systems Littlewood-Paley theory Critical regularity
DOI10.1016/j.jde.2015.05.002
Language英语
Funding ProjectMCM ; NSFC[11371347] ; Chinese Academy of Sciences ; National Center for Mathematics and Interdisciplinary Sciences
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000363434300009
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21070
Collection数学所
Corresponding AuthorZhang, Ping
Affiliation1.Fac Sci Tunis, Dept Math, Tunis 2092, Tunisia
2.Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Hun Loo Keng Key Lab Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Abidi, Hammadi,Zhang, Ping. On the global well-posedness of 2-D inhomogeneous incompressible Nayier Stokes system with variable viscous coefficient[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2015,259(8):3755-3802.
APA Abidi, Hammadi,&Zhang, Ping.(2015).On the global well-posedness of 2-D inhomogeneous incompressible Nayier Stokes system with variable viscous coefficient.JOURNAL OF DIFFERENTIAL EQUATIONS,259(8),3755-3802.
MLA Abidi, Hammadi,et al."On the global well-posedness of 2-D inhomogeneous incompressible Nayier Stokes system with variable viscous coefficient".JOURNAL OF DIFFERENTIAL EQUATIONS 259.8(2015):3755-3802.
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