An anisotropic partial regularity criterion for the Navier-Stokes equations

Abstract

In this paper, we address the partial regularity of suitable weak solutions of the incompressible Navier--Stokes equations. We prove an interior regularity criterion involving only one component of the velocity. Namely, if $(u,p)$ is a suitable weak solution and a certain scale-invariant quantity involving only $u_3$ is small on a space-time cylinder $Q_r(x_0,t_0)$, then $u$ is regular at $(x_0,t_0)$.

15 pages

Cited by in corpus (2)

• On local Type I singularities of the Navier-Stokes equations and Liouville theorems
• Local regularity criteria in terms of one velocity component for the Navier-Stokes equations