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

TL;DR

This paper introduces a new boundary regularity criterion for the 3D Navier--Stokes equations and establishes a bound on the Minkowski dimension of boundary singular points, advancing understanding of boundary regularity.

Contribution

It provides a novel boundary regularity criterion and bounds the Minkowski dimension of boundary singularities in the Navier--Stokes equations.

Findings

New boundary regularity criterion for weak solutions.

Bound on the Minkowski dimension of boundary singular points.

Improved understanding of boundary regularity in Navier--Stokes equations.

Abstract

We study the partial regularity problem of the three-dimensional incompressible Navier--Stokes equations. We present a new boundary regularity criterion for boundary suitable weak solutions. As an application, a bound for the parabolic Minkowski dimension of possible singular points on the boundary is obtained.