Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space $L^2(0,T,W^{1,3}(\varOmega)^3)$ are regular.
@article{119227,
author = {Zden\v ek Skal\'ak and Petr Ku\v cera},
title = {Remark on regularity of weak solutions to the Navier-Stokes equations},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {42},
year = {2001},
pages = {111-117},
zbl = {1038.35061},
mrnumber = {1825376},
language = {en},
url = {http://dml.mathdoc.fr/item/119227}
}
Skalák, Zdeněk; Kučera, Petr. Remark on regularity of weak solutions to the Navier-Stokes equations. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 111-117. http://gdmltest.u-ga.fr/item/119227/
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