Remarks on the singular set of suitable weak solutions for the three-dimensional Navier-Stokes equations

In this study, S denotes the possible interior singular set of suitable weak solutions for the three-dimensional Navier-Stokes equations. We improve the known upper box-counting dimension of this set from 360/277(≈1.300) given by [24] to 975/758 (≈1.286). We also show that Λ(S,r(log⁡(e/r))σ)=0(0≤σ<27/113), which extends the previous corresponding results concerning the improvement of the classical Caffarelli-Kohn-Nirenberg theorem by a logarithmic factor given by Choe and Lewis [3, J. Funct. Anal., 175:348-369, 2000], and by Choe and Yang [4, Comm. Math. Phys., 336:171-198, 2015]. The proof is inspired by a new ε-regularity criterion, which was proved by Guevara and Phuc [7, Calc. Var., 56:68, 2017].