Striated Regularity of 2-D Inhomogeneous Incompressible Navier-Stokes System with Variable Viscosity

doi:10.1007/s00220-019-03446-z

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	Striated Regularity of 2-D Inhomogeneous Incompressible Navier-Stokes System with Variable Viscosity
	Paicu, Marius 1; Zhang, Ping 2,3,4
	2020-05-01
发表期刊	COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN	0010-3616
卷号	376 期号:1 页码:385-439
摘要	In 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.
DOI	10.1007/s00220-019-03446-z
收录类别	SCI
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000530733400011
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51458
专题	中国科学院数学与系统科学研究院
通讯作者	Paicu, Marius
作者单位	1.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
推荐引用方式 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.