Blow-up of critical norms for the 3-D Navier-Stokes equations

被引：0
|
作者：
WANG WenDong [1 ]
ZHANG ZhiFei [2 ]
机构：
[1] School of Mathematical Sciences, Dalian University of Technology
[2] School of Mathematical Sciences, Peking University
来源：
ScienceChina(Mathematics) | 2017年 / 60卷 / 04期
基金：
中国国家自然科学基金; 中央高校基本科研业务费专项资金资助;
关键词：
Navier-Stokes equations; interior regularity criterion; BMO space; Besov space;
D O I：
暂无
中图分类号：
O175 [微分方程、积分方程];
学科分类号：
070104 ;
摘要：
Let u =(uh, u3) be a smooth solution of the 3-D Navier-Stokes equations in R3× [0, T). It was proved that if u3 ∈ L∞(0, T;˙B-1+3/p p,q(R3)) for 3 < p, q < ∞ and uh∈ L∞(0, T; BMO-1(R3)) with uh(T) ∈ VMO-1(R3), then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al.(2016), which requires u ∈ L∞(0, T;˙B-1+3/pp,q(R3)). Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest.
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页码：637 / 650
页数：14
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