An Anisotropic Partial Regularity Criterion for the Navier-Stokes Equations

被引：10
|
作者：
Kukavica, Igor [1 ]
Rusin, Walter [2 ]
Ziane, Mohammed [1 ]
机构：
[1] Univ Southern Calif, Dept Math, Los Angeles, CA 90089 USA
[2] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA
来源：
JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2017年 / 19卷 / 01期
基金：
美国国家科学基金会;
关键词：
SUITABLE WEAK SOLUTIONS; PRESSURE; PROOF;
D O I：
10.1007/s00021-016-0278-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we address the partial regularity of suitable weak solutions of the incompressible Navier-Stokes equations. We prove an interior regularity criterion involving only one component of the velocity. Namely, if (u, p) is a suitable weak solution and a certain scale-invariant quantity involving only u(3) is small on a space-time cylinder Q*(r)(x(0), t(0)), then u is regular at (x(0), t(0)).
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页码：123 / 133
页数：11
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