We consider a two-dimensional Navier-Stokes shear flow with time dependent boundary driving and subject to Tresca law. We establish the existence of a unique global in time solution and then, using a recent method based on the concept of the Kuratowski measure of noncompactness of a bounded set, we prove the existence of the pullback attractor for the associated cocycle. This research is motivated by a problem from lubrication theory.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-5,
author = {Mahdi Boukrouche and Grzegorz \L ukaszewicz},
title = {On the existence of pullback attractor for a two-dimensional shear flow with Tresca's boundary condition},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {81-93},
zbl = {1148.76013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-5}
}
Mahdi Boukrouche; Grzegorz Łukaszewicz. On the existence of pullback attractor for a two-dimensional shear flow with Tresca's boundary condition. Banach Center Publications, Tome 83 (2008) pp. 81-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-5/