Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time
Analysis of PDEs
2009-11-11 v3
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.
Cite
@article{arxiv.math/0601113,
title = {Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time},
author = {Hongjie Dong and Dapeng Du},
journal= {arXiv preprint arXiv:math/0601113},
year = {2009}
}
Comments
19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phys