We present regularity conditions for a solution to the 3D Navier-Stokes equations, the 3D Euler equations and the 2D quasigeostrophic equations, considering the vorticity directions together with the vorticity magnitude. It is found that the regularity of the vorticity direction fields is most naturally measured in terms of norms of the Triebel-Lizorkin type.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-6,
author = {Dongho Chae},
title = {On the conditional regularity of the Navier-Stokes and related equations},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {117-126},
zbl = {1110.35312},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-6}
}
Dongho Chae. On the conditional regularity of the Navier-Stokes and related equations. Banach Center Publications, Tome 72 (2006) pp. 117-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc74-0-6/