A Weak-L p Prodi-Serrin Type Regularity Criterion for the Navier-Stokes Equations

被引：30

作者：

Bosia, Stefano ^{[1
]}

Pata, Vittorino ^{[1
]}

Robinson, James C. ^{[2
]}

机构：

[1] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2014年 / 16卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Navier-Stokes equations; weak solutions; strong solutions; blow-up; regularity criteria; weak Lebesgue spaces;

D O I：

10.1007/s00021-014-0182-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give simple proofs that a weak solution u of the Navier-Stokes equations with H (1) initial data remains strong on the time interval [0, T] if it satisfies the Prodi-Serrin type condition u a L (s) (0, T;L (r,a)(Omega)) or if its L (s,a)(0, T;L (r,a)(Omega)) norm is sufficiently small, where 3 < r a parts per thousand currency sign a and (3/r) + (2/s) = 1.

引用

页码：721 / 725

页数：5

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