A Regularity Criterion for the Navier-Stokes Equations in Terms of One Directional Derivative of the Velocity

被引：7
作者：
Liu, Qiao [1 ]
机构：
[1] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China
来源：
ACTA APPLICANDAE MATHEMATICAE | 2015年 / 140卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Navier-Stokes equations; Regularity; Weak solution; Morrey-Campanato space; WEAK SOLUTIONS;
D O I：
10.1007/s10440-014-9975-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the regularity criterion for the three dimensional incompressible Navier-Stokes equations in terms of one directional derivative of the velocity. The result shows that if weak solution u satisfies partial derivative(3)u is an element of L2/1-r (0, T; (M) Over dot(p,3/r) (R-3)) with 0 < r < 1 and 2 <= p <= 3/r, then u is regular on (0, T] x R-3. Here, is the homogeneous Morrey-Campanato space.
引用
收藏
页码：1 / 9
页数：9
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