In this paper, we obtain local energy decay estimates and $L_p$ - $L_q$ estimates of the solutions to the Stokes equations with Neumann boundary condition which is obtained as a linearized equation of the free boundary problem for the Navier-Stokes equations. Comparing with the non-slip boundary condition case, we have a better decay estimate for the gradient of the semigroup because of the null force at the boundary.
Publié le : 2007-01-14
Classification:
L_p-L_q estimates,
local energy decay,
Stokes semigroup,
Neumann boundary condition,
35Q30,
76D07
@article{1180135499,
author = {SHIBATA, Yoshihiro and SHIMIZU, Senjo},
title = {Decay properties of the Stokes semigroup in exterior domains with Neumann boundary condition},
journal = {J. Math. Soc. Japan},
volume = {59},
number = {1},
year = {2007},
pages = { 1-34},
language = {en},
url = {http://dml.mathdoc.fr/item/1180135499}
}
SHIBATA, Yoshihiro; SHIMIZU, Senjo. Decay properties of the Stokes semigroup in exterior domains with Neumann boundary condition. J. Math. Soc. Japan, Tome 59 (2007) no. 1, pp. 1-34. http://gdmltest.u-ga.fr/item/1180135499/