Decay Results of the Nonstationary Navier-Stokes Flows in Half-Spaces

doi:10.1007/s00205-018-1263-z

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	Decay Results of the Nonstationary Navier-Stokes Flows in Half-Spaces
	Han, Pigong1,2
	2018-12-01
发表期刊	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN	0003-9527
卷号	230 期号:3 页码:977-1015
摘要	There is a long standing problem on the nonstationary Navier-Stokes equations which pertains to how to characterize the L-1-time asymptotic expansion of the Navier-Stokes flows in the half space. Beyond a few partial results, new progress has not yet to be made on this open question. In this article, we give a confirmed answer to this problem; namely, a thorough characterization on L-1-summability is revealed. In order to prove this result, we need to avoid the unboundedness of the projection operator, which is overcome by treating an elliptic Neumann problem. Finally, using the weighted estimates on the heat kernel's convolution, we obtain the exact profile structure of the asymptotic expansion in L1(R+n). In addition, some crucial estimates on the fractional spatial derivatives of the non-stationary Stokes and Navier-Stokes flows are established for the first time, which allows for a better understanding of the L-1-decay problem.
DOI	10.1007/s00205-018-1263-z
语种	英语
WOS研究方向	Mathematics ; Mechanics
WOS类目	Mathematics, Applied ; Mechanics
WOS记录号	WOS:000443822500005
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/30930
专题	应用数学研究所
通讯作者	Han, Pigong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Han, Pigong. Decay Results of the Nonstationary Navier-Stokes Flows in Half-Spaces[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2018,230(3):977-1015.
APA	Han, Pigong.(2018).Decay Results of the Nonstationary Navier-Stokes Flows in Half-Spaces.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,230(3),977-1015.
MLA	Han, Pigong."Decay Results of the Nonstationary Navier-Stokes Flows in Half-Spaces".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 230.3(2018):977-1015.