We present results on local and boundary regularity for weak solutions to the Navier-Stokes equations. Beginning with the regularity criterion proved recently in  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 () or from the regularity of the pressure (). We conclude by presenting regularity criteria near the boundary based on the results in  and .
Submitted August 26, 2003. Published January 13, 2004.
Math Subject Classifications: 35Q35, 35B65.
Key Words: Navier-Stokes equation, weak solution, partial regularity, energy inequality.
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|Zdenek Skalak |
Institute of Hydrodynamics
Czech Academy of Sciences
Pod Patankou 30/5
166 12 Prague 6, Czech Republic
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