On the interior regularity criterion and the number of singular points to the Navier-Stokes equations

Wendong Wang; Zhifei Zhang

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arXiv · 1201.1100

On the interior regularity criterion and the number of singular points to the Navier-Stokes equations

Wendong Wang·Zhifei Zhang

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Abstract

We establish some interior regularity criterions of suitable weak solutions for the 3-D Navier-Stokes equations, which allow the vertical part of the velocity to be large under the local scaling invariant norm. As an application, we improve Ladyzhenskaya-Prodi-Serrin's criterion and Escauriza-Seregin-Šverák's criterion. We also show that if weak solution $u$ satisfies $$ \|u(\cdot,t)\|_{L^p}\leq C(-t)^{\frac {3-p}{2p}} $$ for some $3<p<\infty$, then the number of singular points is finite.

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Wendong Wang, Zhifei Zhang. 2012-01-05. On the interior regularity criterion and the number of singular points to the Navier-Stokes equations. https://arxiv.org/abs/1201.1100

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