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

TL;DR

This paper improves the upper bound on the Minkowski dimension of interior singular points in 3D incompressible Navier-Stokes solutions, also extending results to magnetohydrodynamics.

Contribution

It provides a sharper upper bound of 95/63 for the Minkowski dimension of singular sets and extends the analysis to magnetohydrodynamic equations.

Findings

Upper bound of 95/63 for Minkowski dimension of singular points

Results applicable to magnetohydrodynamic equations

Enhanced understanding of singular set structure in fluid dynamics

Abstract

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 $95/63$. The result also continue to hold for the three dimensional incompressible magnetohydrodynamic equations without any difficulty.