Partial Regularity of solutions to the Four-Dimensional Navier-Stokes Equations

被引：14
|
作者：
Dong, Hongjie [1 ]
Gu, Xumin [2 ]
机构：
[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA
[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 11卷 / 01期
基金：
美国国家科学基金会;
关键词：
Navier-Stokes equations; partial regularity; Hausdorff's dimension; SUITABLE WEAK SOLUTIONS; PROOF;
D O I：
10.4310/DPDE.2014.v11.n1.a3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider suitable weak solutions of incompressible Navier-Stokes equations in four spatial dimensions. We obtain two "regularity criteria in terms of certain scale-invariant quantities. As a consequence, we show that the two-dimensional space-time Hausdorff measure of the set of singular points is equal to zero.
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页码：53 / 69
页数：17
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