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arXiv · 1511.02807

An anisotropic partial regularity criterion for the Navier-Stokes equations

I. Kukavica·W. Rusin·M. Ziane
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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 $(x_0,t_0)$.

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I. Kukavica, W. Rusin, M. Ziane. 2015-11-09. An anisotropic partial regularity criterion for the Navier-Stokes equations. https://doi.org/10.1007/s00021-016-0278-1

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