We obtain a regularity conditions for solutions of the 3D
Navier-Stokes equations with fractional powers of the Laplacian,
which incorporates the vorticity direction and its magnitude
simultaneously. We find that regularity assumption of direction
field of the vorticity compensates with the integrability
condition for the magnitude of vorticity. The regularity of
direction field is most naturally measured in terms of the
Triebel-Lizorkin type of norms. This unifies and extends previous
results in this direction of studies, where the geometric
structure of the vortex stretching term is used to obtain refined
regularity conditions, initiated by Constantin and Fefferman.
Publié le : 2007-04-14
Classification:
Navier-Stokes equations,
regularity conditions,
Triebel-Lizorkin type of spaces,
35Q30,
76D03,
76D05
@article{1180728897,
author = {Chae, Dongho},
title = {On the Regularity Conditions for the Navier-Stokes and Related Equations},
journal = {Rev. Mat. Iberoamericana},
volume = {23},
number = {1},
year = {2007},
pages = { 371-384},
language = {en},
url = {http://dml.mathdoc.fr/item/1180728897}
}
Chae, Dongho. On the Regularity Conditions for the Navier-Stokes and Related Equations. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp. 371-384. http://gdmltest.u-ga.fr/item/1180728897/