Global and regular solutions of the Navier-Stokes system in cylindrical domains have already been obtained under the assumption of smallness of (1) the derivative of the velocity field with respect to the variable along the axis of cylinder, (2) the derivative of force field with respect to the variable along the axis of the cylinder and (3) the projection of the force field on the axis of the cylinder restricted to the part of the boundary perpendicular to the axis of the cylinder. With the same assumptions we prove in this paper the existence of a global attractor for the Navier-Stokes equations and convergence of solutions to the stationary solutions for the large viscosity coefficient.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-2-6,
author = {Bernard Nowakowski and Wojciech M. Zaj\k aczkowski},
title = {Global attractor for Navier-Stokes equations in cylindrical domains},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {183-194},
zbl = {1170.35494},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-2-6}
}
Bernard Nowakowski; Wojciech M. Zajączkowski. Global attractor for Navier-Stokes equations in cylindrical domains. Applicationes Mathematicae, Tome 36 (2009) pp. 183-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-2-6/