We consider the time-periodic Oseen flow around a rotating body in ℝ³. We prove a priori estimates in -spaces of weak solutions for the whole space problem under the assumption that the right-hand side has the divergence form. After a time-dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional term -(ω ∧ x)·∇u + ω ∧ u in the equation of momentum where ω denotes the angular velocity. We prove the existence of generalized weak solutions in -space using Littlewood-Paley decomposition and maximal operators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-17,
author = {Stanislav Kra\v cmar and \v S\'arka Ne\v casov\'a and Patrick Penel},
title = {$L^q$-approach to weak solutions of the Oseen flow around a rotating body},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {259-276},
zbl = {1148.76017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-17}
}
Stanislav Kračmar; Šárka Nečasová; Patrick Penel. $L^q$-approach to weak solutions of the Oseen flow around a rotating body. Banach Center Publications, Tome 83 (2008) pp. 259-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-17/