Electron. J. Diff. Eqns., Vol. 2004(2004), No. 09, pp. 1-14.

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

Zdenek Skalak

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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