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

Abstract

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 upper box dimension of interior singular points and boundary singular points are bounded by $7/6$ and $10/9$, respectively. Both proofs rely on recent progress of $\epsilon$-regularity criteria at one scale.

16 pages

Cited by in corpus (3)

• Local regularity of weak solutions of the hypodissipative Navier-Stokes equations
• Partial regularity of Leray-Hopf weak solutions to the incompressible Navier-Stokes equations with hyperdissipation
• Boundary $\epsilon$-regularity criteria for the 3D Navier-Stokes equations