We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer . Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded -calculus for the associated Stokes operator and some of its consequences, which also yields an application to a free boundary value problem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-1,
author = {Helmut Abels},
title = {Stokes equations in asymptotically flat layers},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {9-19},
zbl = {1101.35344},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-1}
}
Helmut Abels. Stokes equations in asymptotically flat layers. Banach Center Publications, Tome 68 (2005) pp. 9-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-1/