Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 45, pp. 1-11.

Title: Regularity of weak solutions of the Navier-Stokes
       equations near the smooth boundary

Author: Zdenek Skalak (Czech Technical Univ., Czech Republic)

Abstract: 
 Any weak solution $u$ of the Navier-Stokes equations in
 a bounded domain satisfying the Prodi-Serrin's conditions
 locally near the smooth boundary cannot have singular
 points there. This local-up-to-the-boundary boundedness
 of $u$ in space-time implies the H\"{o}lder continuity
 of $u$ up-to-the-boundary in the space variables.
 
Submitted May 19, 2004. Published April 24, 2005.
Math Subject Classifications: 35Q35, 35B65.
Key Words: Navier-Stokes equations; weak solutions; boundary regularity.