The BKM criterion for the 3D Navier-Stokes equations via two velocity components

被引：37

作者：

Dong, Bo-Qing ^{[1
]}

Zhang, Zhifei ^{[2
]}

机构：

[1] Anhui Univ, Sch Math Sci, Hefei 230039, Peoples R China

[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2010年 / 11卷 / 04期

关键词：

Navier-Stokes equations; Beale-Kato-Majda criterion; WEAK SOLUTIONS; REGULARITY CRITERION;

D O I：

10.1016/j.nonrwa.2009.07.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the study of the regularity criterion of Leray-Hopf weak solutions to the 3D Navier-Stokes equations, the Beale-Kato-Majda type criterion is obtained in terms of the horizontal derivatives of the two velocity components integral(T)(0) parallel to del(h (u) over tilde (S))parallel to(B over dot infinity,infinity 0) ds < infinity, <(u)over tilde> = (u(1), u(2), 0), del(h)(u) over tilde = (partial derivative(1)(u) over tilde, partial derivative(2)(u) over tilde, 0). (C) 2010 Published by Elsevier Ltd

引用

页码：2415 / 2421

页数：7

共 25 条

[1]

[Anonymous], 1993, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals

[2]

[Anonymous], 2010, Theory of Function Spaces

[3] REMARKS ON THE BREAKDOWN OF SMOOTH SOLUTIONS FOR THE 3-D EULER EQUATIONS [J].

BEALE, JT ;

KATO, T ;

MAJDA, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1984, 94 (01) :61-66

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

CAFFARELLI, L ;

KOHN, R ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1982, 35 (06) :771-831

[5] Regularity Criteria for the Three-dimensional Navier-Stokes Equations [J].

Cao, Chongsheng ;

Titi, Edriss S. .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (06) :2643-2661

[6]

Chemin J. -Y., 1998, Perfect Incompressible Fluids

[7] Homogeneity Criterion for the Navier-Stokes Equations in the Whole Spaces [J].

Chen, Zhi Min ;

Xin, Zhouping .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2001, 3 (02) :152-182

[8]

daVeiga HB, 1995, CHINESE ANN MATH B, V16, P407

[9] Regularity criterion of weak solutions to the 3D Navier-Stokes equations via two velocity components [J].

Dong, Bo-Qing ;

Chen, Zhi-Min .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (01) :1-10

[10] ON THE NAVIER-STOKES INITIAL VALUE PROBLEM .1. [J].

FUJITA, H ;

KATO, T .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1964, 16 (04) :269-315

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