Decay properties for the incompressible Navier-Stokes flows in a half space

doi:10.1017/prm.2021.63

CSpace > 应用数学研究所

	Decay properties for the incompressible Navier-Stokes flows in a half space
	Han, Pigong1,2
	2021-10-11
发表期刊	PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN	0308-2105
页码	24
摘要	In this article, we give a comprehensive characterization of L-1-summability for the Navier-Stokes flows in the half space, which is a long-standing problem. The main difficulties are that L-q - L-r estimates for the Stokes flow don't work in this end-point case: q = r = 1; the projection operator P : L-1 -> L-sigma(1) is not bounded any more; useful information on the pressure function is missing, which arises in the net force exerted by the fluid on the noncompact boundary. In order to achieve our aims, by making full use of the special structure of the half space, we decompose the pressure function into two parts. Then the knotty problem of handling the pressure term can be transformed into establishing a crucial and new weighted L-1-estimate, which plays a fundamental role. In addition, we overcome the unboundedness of the projection P by solving an elliptic problem with homogeneous Neumann boundary condition.
关键词	Navier-Stokes flow Stokes operator half space
DOI	10.1017/prm.2021.63
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11871457] ; K. C. Wong Education Foundation ; Chinese Academy of Sciences ; Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences[2008DP173182]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000785651700001
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60326
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 properties for the incompressible Navier-Stokes flows in a half space[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,2021:24.
APA	Han, Pigong.(2021).Decay properties for the incompressible Navier-Stokes flows in a half space.PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,24.
MLA	Han, Pigong."Decay properties for the incompressible Navier-Stokes flows in a half space".PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS (2021):24.