Partial Regularity of solutions to the Four-Dimensional Navier-Stokes Equations

摘要

In this paper, we consider suitable weak solutions of incompressible Navier-Stokes equations in four spatial dimensions. We obtain two eregularity 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.