A logarithmically improved regularity criterion for the Navier-Stokes equations

被引：0

作者：

Liu, Qiao ^{[1
]}

Zhao, Jihong ^{[1
]}

Cui, Shangbin ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2012年 / 167卷 / 3-4期

基金：

中国国家自然科学基金;

关键词：

Navier-Stokes equations; Regularity; Mild solution; SPACES;

D O I：

10.1007/s00605-011-0313-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we prove a logarithmically improved regularity criterion in terms of the Besov space norm for the Navier-Stokes equations. The result shows that if a mild solution u satisfies for some 0 a parts per thousand currency sign r < 1 and , then u is regular at t = T.

引用

页码：503 / 509

页数：7

共 16 条

[1]

Cannone M, 2004, HANDBOOK OF MATHEMATICAL FLUID DYNAMICS, VOL 3, P161

[2]

Chan CH, 2007, METHODS APPL ANAL, V14, P197

[3]

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

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

FUJITA, H ;

KATO, T .

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

[5] SOLUTIONS FOR SEMILINEAR PARABOLIC EQUATIONS IN LP AND REGULARITY OF WEAK SOLUTIONS OF THE NAVIER-STOKES SYSTEM [J].

GIGA, Y .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1986, 62 (02) :186-212

[6] Bilinear estimates in BMO and the Navier-Stokes equations [J].

Kozono, H ;

Taniuchi, Y .

MATHEMATISCHE ZEITSCHRIFT, 2000, 235 (01) :173-194

[7] Bilinear estimates in homogeneous Triebel-Lizorkin spaces and the Navier-Stokes equations [J].

Kozono, H ;

Shimada, Y .

MATHEMATISCHE NACHRICHTEN, 2004, 276 :63-74

[8] The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations [J].

Kozono, H ;

Ogawa, T ;

Taniuchi, Y .

MATHEMATISCHE ZEITSCHRIFT, 2002, 242 (02) :251-278

[9]

Lemarie-Rieusset P.-G., 2002, Research Notes in Mathematics, V431

[10] On the movement of a viscous fluid to fill the space [J].

Leray, J .

ACTA MATHEMATICA, 1934, 63 (01) :193-248

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