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

Abstract

In this paper, by invoking the appropriate decomposition of pressure to exploit the energy hidden in pressure, we present some new ε-regularity criteria for suitable weak solutions of the 3D Navier–Stokes equations at one scale: for any p, q∈ [1 , ∞] satisfying 1 ≤ 2 / q+ 3 / p< 2 , there exists an absolute positive constant ε such that u∈ L∞(Q(1 / 2)) if ‖u‖Lp,q(Q(1))+‖Π‖L1(Q(1))