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.

引用

页码：53 / 69

页数：17

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