Dynamics of Partial Differential Equations
Volume 11 (2014)
Partial regularity of solutions to the four-dimensional Navier-Stokes equations
Pages: 53 – 69
In this paper, we consider suitable weak solutions of incompressible Navier-Stokes equations in four spatial dimensions. We obtain two $\epsilon$ 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.
Navier-Stokes equations, partial regularity, Hausdorff’s dimension
2010 Mathematics Subject Classification
35Q30, 76D03, 76D05