We study the Oseen problem with rotational effect in exterior three-dimensional domains. Using a variational approach we prove existence and uniqueness theorems in anisotropically weighted Sobolev spaces in the whole three-dimensional space. As the main tool we derive and apply an inequality of the Friedrichs-Poincaré type and the theory of Calderon-Zygmund kernels in weighted spaces. For the extension of results to the case of exterior domains we use a localization procedure.
@article{1265380430,
author = {KRA\v CMAR, Stanislav and NE\v CASOV\'A, \v S\'arka and PENEL, Patrick},
title = {Anisotropic $L^{2}$ -estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body},
journal = {J. Math. Soc. Japan},
volume = {62},
number = {1},
year = {2010},
pages = { 239-268},
language = {en},
url = {http://dml.mathdoc.fr/item/1265380430}
}
KRAČMAR, Stanislav; NEČASOVÁ, Šárka; PENEL, Patrick. Anisotropic $L^{2}$ -estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body. J. Math. Soc. Japan, Tome 62 (2010) no. 1, pp. 239-268. http://gdmltest.u-ga.fr/item/1265380430/