A $\epsilon$-regularity criterion without pressure of suitable weak solutions to the Navier-Stokes equations at one scale

Abstract

In this paper, we continue our work in [15] to derive ε-regularity criteria at one scale without pressure for suitable weak solutions to the Navier-Stokes equations. We establish a $\epsilon$-regularity criterion below of suitable weak solutions, for any $\delta >0$, $${\iint }_{Q(1)}|u{|}^{\frac{5}{2}+\delta }dxdt\le \epsilon .$$ As an application, we extend the previous corresponding results concerning the improvement of the classical Caffarelli--Kohn--Nirenberg theorem by a logarithmic factor.

27 pages. arXiv admin note: text overlap with arXiv:1805.04841