Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved -estimates of second order derivatives uniformly in the angular and translational velocities, ω and k, of the obstacle, whereas the transport terms fails to have -estimates independent of ω. In this paper we clarify this unexpected behavior and prove weighted -estimates of first order terms independent of ω.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-5,
author = {Reinhard Farwig},
title = {Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {73-84},
zbl = {1101.35348},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-5}
}
Reinhard Farwig. Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle. Banach Center Publications, Tome 68 (2005) pp. 73-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-5/