article

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

Authors: Hongjie Dong and Robert M. Strain

Issue: Volume 61 (2012), Issue 6, 2211-2229

Abstract:

$Consider steady-state weak solutions to the incompressible Navier-Stokes equations in six spatial dimensions. We prove that the 2D Hausdorff measure of the set of singular points is equal to zero. This problem was mentioned in 1988 by Struwe [M. Struwe, \textit{On partial regularity results for the Navier-Stokes equations}, Comm. Pure Appl. Math. \textbf{41} (1988), no. 4, 437--458], during his study of the five-dimensional case.$