We study the motion of a viscous incompressible fluid filling the whole three-dimensional space exterior to a rigid body, that is rotating with constant angular velocity ω, under the action of external force f. By using a frame attached to the body, the equations are reduced to (1.1) in a fixed exterior domain D. Given f = divF with , we consider this problem in D × ℝ and prove that there exists a unique solution when F and |ω| are sufficiently small. If, in particular, the external force for the original problem is independent of t, then f is periodic with period 2π/|ω|. In this situation, as a corollary of our result, we obtain a periodic solution with the same period. Stability of our solution is also discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-9,
author = {Toshiaki Hishida},
title = {THE Navier-stokes flow around a rotating obstacle with time-dependent body force},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {149-162},
zbl = {1179.35216},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-9}
}
Toshiaki Hishida. THE Navier-stokes flow around a rotating obstacle with time-dependent body force. Banach Center Publications, Tome 86 (2009) pp. 149-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-9/