On Wolf's regularity criterion of suitable weak solutions to the Navier-Stokes equations

In this paper, we consider the local regularity of suitable weak solutions to the 3D incompressible Navier-Stokes equations. By means of the local pressure projection introduced by Wolf in [15,16], we present a $\epsilon$-regularity criterion below of suitable weak solutions $${\iint }_{Q(1)}\mathrm{\mid }u{\mathrm{\mid }}^{20\mathrm{/}7}dxdt\le \epsilon ,$$ which gives an improvement of previous corresponding results obtained in Chae and Wolf [3, Arch. Ration. Mech. Anal., 225: 549-572, 2017], in Guevara and Phuc [6, Calc. Var., 56:68, 2017] and in Wolf [16, Ann. Univ. Ferrara, 61: 149-171, 2015].