Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time
arXiv:math/0601113 · doi:10.1007/s00220-007-0259-6
Abstract
The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.
19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phys