KMS Of Academy of mathematics and systems sciences, CAS
| Decay properties for the incompressible Navier-Stokes flows in a half space | |
Han, Pigong1,2
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| 2021-10-11 | |
| Source Publication | PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
 |
| ISSN | 0308-2105 |
| Pages | 24 |
| Abstract | 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. |
| Keyword | Navier-Stokes flow Stokes operator half space |
| DOI | 10.1017/prm.2021.63 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000785651700001 |
| Publisher | CAMBRIDGE UNIV PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60326 |
| Collection | 应用数学研究所 |
| Corresponding Author | Han, Pigong |
| Affiliation | 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 |
| Recommended Citation 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. |
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