On regularity and singularity for L∞ (0, T; L3,w(R3)) solutions to the Navier-Stokes equations

被引：0

作者：

Choe, Hi Jun ^{[1
]}

Wolf, Jorg ^{[2
]}

Yang, Minsuk ^{[1
]}

机构：

[1] Yonsei Univ, Dept Math, Yonseiro 50, Seoul, South Korea

[2] Chung Ang Univ, Dept Math, Heukseokro 84, Seoul, South Korea

来源：

MATHEMATISCHE ANNALEN | 2020年 / 377卷 / 1-2期

基金：

新加坡国家研究基金会;

关键词：

35Q35; 35D30; 35B65; SUITABLE WEAK SOLUTIONS; CRITERIA;

D O I：

10.1007/s00208-019-01843-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study local regularity properties of a weak solution u to the Cauchy problem of the incompressible Navier-Stokes equations. We present a new regularity criterion for the weak solution u satisfying the condition L infinity(0,T;L3,w(R3)) without any smallness assumption on that scale, where L3,w(R3) denotes the standard weak Lebesgue space. As an application, we conclude that there are at most a finite number of blowup points at any singular time t.

引用

页码：617 / 642

页数：26

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