The Minkowski dimension of interior singular points in the incompressible Navier--Stokes equations

We study the possible interior singular points of suitable weak solutions to the three dimensional incompressible Navier–Stokes equations. We present an improved parabolic upper Minkowski dimension of the possible singular set. It is bounded by $95\mathrm{/}63$. The result also continue to hold for the three dimensional incompressible magnetohydrodynamic equations without any difficulty.