Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 120, pp. 1-6.
Title: Remark on the spatial regularity for the Navier-Stokes equations
Author: Cheng He (Academia Sinica, Beijing, China)
Abstract:
Let u be a Leray-Hopf weak solution to the Navier-Stokes
equations. We will show that the set of possible singular
points of the vector field resulting from
integrating the velocity u with respect to time
has Hausdorff dimension zero.
Submitted November 24, 2006. Published August 28, 2008.
Math Subject Classifications: 35Q76D
Key Words: Partial regularity; Navier-Stokes equations;
Leray-Hopf weak solution.
An addendum was posted on September 30, 2008.
It modifies the proof of the main theorem.
Please see the last page of this manuscript.