Institute of Hydrodynamics
Czech Academy of Sciences
Pod Patankou 30/5
166 12 Prague 6, Czech Republic
email: skalak@mat.fsv.cvut.cz skalak@ih.cas.cz
Zdenek Skalak
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.
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Zdenek Skalak Institute of Hydrodynamics Czech Academy of Sciences Pod Patankou 30/5 166 12 Prague 6, Czech Republic email: skalak@mat.fsv.cvut.cz skalak@ih.cas.cz |
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