On partial regularity for weak solutions to the Navier-Stokes equations
文献类型：期刊论文
| 作者 | He, C |
| 刊名 | JOURNAL OF FUNCTIONAL ANALYSIS
 |
| 出版日期 | 2004-06-01 |
| 卷号 | 211期号:1页码:153-162 |
| 关键词 | Navier-Stokes equations partial regularity |
| ISSN号 | 0022-1236 |
| DOI | 10.1016/j.jfa.2003.06.009 |
| 英文摘要 | 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. |
| 语种 | 英语 |
| WOS记录号 | WOS:000221422600003 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/485]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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