On the possible time singularities for the 3D Navier-Stokes equations

PHYSICA D-NONLINEAR PHENOMENA

卷:395

Article

Luo, Xiaoyutao¹ 

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

关键词: Navier-Stokes equations;    Leray-Hopf weak solutions;    time singularities;   

DOI  :  10.1016/j.physd.2019.02.008

来源: Elsevier

【 摘 要 】

We prove a local-in-time regularity criterion for the 3D Navier-Stokes equations. In particular, it follows from the criterion that the Hausdorff dimension of possible singular times of Leray-Hopf weak solutions u is an element of (LtBS, infinity alpha)-B-r for some alpha > 0, s > 3 and r > 2 is less than r/2(3/s+2/r-alpha-1). The main contribution is that we do not assume the suitability of weak solutions. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free