An $\text{eps}$-regularity criterion at one scale for 3-D Navier-Stokes equations and improved upper bound on the box dimension of the interior singular set

In this paper, we obtain an $\epsilon$-regularity criterion at one scale for 3D Navier-Stokes equations using a coarse-to-refined estimate argument based on mean-fluctuation decomposition. Making use of this $\epsilon$-regularity criterion, we improve the upper bound on the box dimension of the interior singular set to $15\mathrm{/}13$.