Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations
文献类型：期刊论文
| 作者 | He, C; Xin, ZP |
| 刊名 | JOURNAL OF FUNCTIONAL ANALYSIS
 |
| 出版日期 | 2005-10-01 |
| 卷号 | 227期号:1页码:113-152 |
| 关键词 | magnetohydrodynamics equations partial regularity |
| ISSN号 | 0022-1236 |
| DOI | 10.1016/j.jfa.2005.06.009 |
| 英文摘要 | In this paper, we study the local behavior of the solutions to the three-dimensional magnetohydrodynamic equations. we are interested in both the uniform gradient estimates for smooth solutions and regularity of weak solutions. It is shown that, in some neighborhood of (x(0), t(0)), the gradients of the velocity field u and the magnetic field B are locally uniformly bounded in L-infinity norm as long as that either the scaled local L-2-norm of the gradient or the scaled local total energy of the velocity field is small, and the scaled local total energy of the magnetic field is uniformly bounded. These estimates indicate that the velocity field plays a more dominant role than that of the magnetic field in the regularity theory. As an immediately corollary we can derive an estimates of Hausdorff dimension on the possible singular set of a suitable weak solution as in the case of pure fluid. Various partial regularity results are obtained as consequences of our blow-up estimates. (c) 2005 Elsevier Inc. All rights reserved. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000232077600004 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1917]  |
| 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 | 1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China 3.Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China |
| 推荐引用方式 GB/T 7714 | He, C,Xin, ZP. Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2005,227(1):113-152. |
| APA | He, C,&Xin, ZP.(2005).Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations.JOURNAL OF FUNCTIONAL ANALYSIS,227(1),113-152. |
| MLA | He, C,et al."Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations".JOURNAL OF FUNCTIONAL ANALYSIS 227.1(2005):113-152. |
入库方式： OAI收割
来源：数学与系统科学研究院
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