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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（4）
• 页码范围: 637-650
• 页数: 14页
• 语种: 英文
• DOI: 10.1007/s11425-016-0344-5

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-1p,1q+3/p(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-1p,1q+3/p(R3)).Our proof is based on a new interior regularity criterion in terms of one velocity component,which is independent of interest.