On partial regularity of steady-state solutions to the 6D Navier-Stokes equations

TL;DR

This paper proves that the set of singular points in steady-state solutions to the 6D Navier-Stokes equations has zero 2D Hausdorff measure, extending partial regularity results to higher dimensions.

Contribution

It establishes the first partial regularity result for steady-state solutions in six dimensions, confirming the singular set's measure is zero.

Findings

Singular set has zero 2D Hausdorff measure in 6D

Extends partial regularity results from 5D to 6D

Addresses a problem posed by Struwe in 1988

Abstract

Consider steady-state weak solutions to the incompressible Navier-Stokes equations in six spatial dimensions. We prove that the 2D Hausdorff measure of the set of singular points is equal to zero. This problem was mentioned in 1988 by Struwe [24], during his study of the five dimensional case.