Improved bounds for box dimensions of potential singular points to the Navier-Stokes equations

摘要

In this paper, we study the potential singular points of interior and boundary suitable weak solutions to the 3D Navier-Stokes equations. It is shown that the upper box dimensions of interior singular points and boundary singular points are bounded by 7/6 and 10/9, respectively. Both proofs rely on the recent progress of -regularity criteria at one scale.