Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

Details Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

2006-01-06

arxiv.org/abs/math/0601113v3

Mathematics

Analysis of PDEs

19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phys

Scientific paper

10.1007/s00220-007-0259-6

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.

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