On the box-counting dimension of potential singular set for suitable weak solutions to the 3D Navier-Stokes equations

In this paper, we are concerned with the upper box-counting dimension of the set of possible singular points in space-time of suitable weak solutions to the 3D Navier-Stokes equations. By taking full advantage of the pressure $\mathrm{\Pi }$ in terms of $\mathrm{\nabla }\mathrm{\Pi }$ in equations, we show that this upper box dimension is at most $135\mathrm{/}104(\approx 1.30)$, which improves the known upper box-counting dimension $95\mathrm{/}63(\approx 1.51)$ in Koh et al. [9, J. Differential Equations, 261: 3137–3148, 2016], $45\mathrm{/}29(\approx 1.55)$ in Kukavica et al. [11, Nonlinearity 25: 2775-2783, 2012] and $135\mathrm{/}82(\approx 1.65)$ in Kukavica [10, Nonlinearity 22: 2889-2900, 2009].