Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations

doi:10.1016/j.jfa.2005.06.009

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	Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations
	He, C ; Xin, ZP
	2005-10-01
发表期刊	JOURNAL OF FUNCTIONAL ANALYSIS
ISSN	0022-1236
卷号	227 期号:1 页码:113-152
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.
关键词	magnetohydrodynamics equations partial regularity
DOI	10.1016/j.jfa.2005.06.009
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000232077600004
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1918
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.