Navier-Stokes equations with regularity in one direction

被引：146

作者：

Kukavica, Igor ^{[1
]}

Ziane, Mohammed ^{[1
]}

机构：

[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2007年 / 48卷 / 06期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1063/1.2395919

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider sufficient conditions for the regularity of Leray-Hopf solutions of the Navier-Stokes equations. We prove that if the third derivative of the velocity partial derivative u/partial derivative x(3) belongs to the space (Lt0Lx0r)-L-s, where 2/s(0)+3/r(0)<= 2 and 9/4 <= r(0)<= 3, then the solution is regular. This extends a result of Beirao da Veiga [Chin. Ann. Math., Ser. B 16, 407-412 (1995); C. R. Acad. Sci, Ser. I: Math. 321, 405-408 (1995)] by making a requirement only on one direction of the velocity instead of on the full gradient. The derivative partial derivative u/partial derivative x(3) can be substituted with any directional derivative of u. (c) 2007 American Institute of Physics.

引用

页数：10

共 20 条

[1]

[Anonymous], 2002, METHODS APPL ANAL, DOI DOI 10.4310/MAA.2002.V9.N4.A5

[2]

[Anonymous], 2003, USP MAT NAUK

[3] PARTIAL REGULARITY OF SUITABLE WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS [J].