New ε-Regularity Criteria of Suitable Weak Solutions of the 3D Navier-Stokes Equations at One Scale

In this paper, by invoking the appropriate decomposition of pressure to exploit the energy hidden in pressure, we present some new epsilon-regularity criteria for suitable weak solutions of the 3D Navier-Stokes equations at one scale: for any p, q is an element of [1, infinity] satisfying 1 <= 2/q + 3/p < 2, there exists an absolute positive constant epsilon such that u is an element of L-infinity(Q(1/2)) if parallel to u parallel to(Lp,q) ((Q(1))) + parallel to Pi parallel to(L1(Q(1))) < epsilon. This is an improvement of corresponding results recently proved by Guevara and Phuc (Calc Var 56:68, 2017). As an application of these epsilon-regularity criteria, we improve the known upper box dimension of the possible interior singular set of suitable weak solutions of the Navier-Stokes system from 975/758(approximate to 1.286) (Ren et al. in J Math Anal Appl 467:807-824, 2018) to 2400/1903(approximate to 1.261).