Partial regularity of solutions to the four-dimensional Navier-Stokes equations

Abstract

In this paper, we consider suitable weak solutions of incompressible Navier-Stokes equations in four spatial dimensions. We obtain two ε-regularity criteria in terms of certain scale-invariant quantities. As a consequence, we show that the two-dimensional space-time Hausdorff measure of the set of singular points is equal to zero. © 2014 International Press.