In this paper, we study the nonstationary Stokes equation with Neumann boundary condition in a bounded or an exterior domain in ℝⁿ, which is the linearized model problem of the free boundary value problem. Mainly, we prove estimates for the semigroup of the Stokes operator. Comparing with the non-slip boundary condition case, we have the better decay estimate for the gradient of the semigroup in the exterior domain case because of the null force at the boundary.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-15,
author = {Yoshihiro Shibata and Senjo Shimizu},
title = {On the Stokes equation with Neumann boundary condition},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {239-250},
zbl = {1100.35081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-15}
}
Yoshihiro Shibata; Senjo Shimizu. On the Stokes equation with Neumann boundary condition. Banach Center Publications, Tome 68 (2005) pp. 239-250. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-15/