On partial regularity for weak solutions to the Navier-Stokes equations

doi:10.1016/j.jfa.2003.06.009

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	On partial regularity for weak solutions to the Navier-Stokes equations
	He, C
	2004-06-01
发表期刊	JOURNAL OF FUNCTIONAL ANALYSIS
ISSN	0022-1236
卷号	211 期号:1 页码:153-162
摘要	In this paper, we study the partial regularity of the general weak solution u is an element of L-x (0, T; L-2(Omega)) boolean AND L-2 (0, T; H-1(Omega)) to the Navier-Stokes equations, which include the well-known Leray-Hopf weak solutions. It is shown that there is a absolute constant epsilon such that for the weak solution it, if either the scaled local L-q(1 less than or equal to q less than or equal to 2) norm of the gradient of the solution, or the scaled local L-q(1 less than or equal to q less than or equal to 10/3) norm of u is less than epsilon, then u is locally bounded. This implies that the one-dimensional Hausdorff measure is zero for the possible singular point set, which extends the corresponding result due to Caffarelli et al. (Comm. Pure Appl. Math. 35 (1982) 717) to more general weak solution. (C) 2003 Elsevier Inc. All rights reserved.
关键词	Navier-Stokes equations partial regularity
DOI	10.1016/j.jfa.2003.06.009
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000221422600003
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/486
专题	中国科学院数学与系统科学研究院
通讯作者	He, C
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	He, C. On partial regularity for weak solutions to the Navier-Stokes equations[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2004,211(1):153-162.
APA	He, C.(2004).On partial regularity for weak solutions to the Navier-Stokes equations.JOURNAL OF FUNCTIONAL ANALYSIS,211(1),153-162.
MLA	He, C."On partial regularity for weak solutions to the Navier-Stokes equations".JOURNAL OF FUNCTIONAL ANALYSIS 211.1(2004):153-162.