Weighted regularity criteria for the three-dimensional Navier-Stokes equations

被引：13

作者：

Zhou, Yong ^{[1
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2009年 / 139卷

关键词：

WEAK SOLUTIONS; PARABOLIC EQUATIONS; PRESSURE; TERMS; GRADIENT;

D O I：

10.1017/S0308210507000790

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish some regularity criteria in terms of the velocity field with weight for the Navier-Stokes equations in R(3). It is proved that if the weak solution satisfies (x0 is an element of R3)sup parallel to vertical bar x - x(0)vertical bar(beta)u(x, t)parallel to L(alpha)((0,T),L(gamma)(R(3))) < infinity with 2/alpha + 3/gamma = 1 - beta or (x0 is an element of R3)sup parallel to vertical bar x - x(0)vertical bar(beta)del u(x, t)parallel to L(alpha)((0,T), L(gamma)(R(3))) < infinity with 2/alpha + 3/gamma = 2 - beta, then the weak solution actually is regular up to time T.

引用

页码：661 / 671

页数：11

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