Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 09, pp. 1-14.

Title: Commentary on local and boundary regularity of weak solutions to
       Navier-Stokes equations

Author: Zdenek Skalak (Czech Academy of Sciences, Czech Republic)

Abstract: 
 We present results on local and boundary regularity for weak
 solutions to the Navier-Stokes equations. Beginning with the regularity
 criterion proved recently in [14] for the Cauchy problem,
 we show that this criterion holds also locally.
 This is also the case for some other results: We present two examples
 concerning the regularity of weak solutions stemming from the regularity
 of two components of the vorticity ([2]) or from the regularity
 of the pressure ([3]). We conclude by presenting regularity
 criteria near the boundary  based on the results  in [10] and [16].


Submitted August 26, 2003. Published January 13, 2004.
Math Subject Classifications: 35Q35, 35B65.
Key Words: Navier-Stokes equation; weak solution; partial regularity;
           energy inequality.