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.