# THE Navier-stokes flow around a rotating obstacle with time-dependent body force

• Volume: 86, Issue: 1, page 149-162
• ISSN: 0137-6934

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## Abstract

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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 $F\in BUC\left(ℝ;{L}_{3/2,\infty }\left(D\right)\right)$, we consider this problem in D × ℝ and prove that there exists a unique solution $u\in BUC\left(ℝ;{L}_{3,\infty }\left(D\right)\right)$ 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.

## How to cite

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Toshiaki Hishida. "THE Navier-stokes flow around a rotating obstacle with time-dependent body force." Banach Center Publications 86.1 (2009): 149-162. <http://eudml.org/doc/282523>.

@article{ToshiakiHishida2009,
abstract = {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 $F ∈ BUC(ℝ;L_\{3/2,∞\}(D))$, we consider this problem in D × ℝ and prove that there exists a unique solution $u ∈ BUC(ℝ;L_\{3,∞\}(D))$ 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.},
author = {Toshiaki Hishida},
journal = {Banach Center Publications},
keywords = {Navier-Stokes flow; rotating obstacles},
language = {eng},
number = {1},
pages = {149-162},
title = {THE Navier-stokes flow around a rotating obstacle with time-dependent body force},
url = {http://eudml.org/doc/282523},
volume = {86},
year = {2009},
}

TY - JOUR
AU - Toshiaki Hishida
TI - THE Navier-stokes flow around a rotating obstacle with time-dependent body force
JO - Banach Center Publications
PY - 2009
VL - 86
IS - 1
SP - 149
EP - 162
AB - 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 $F ∈ BUC(ℝ;L_{3/2,∞}(D))$, we consider this problem in D × ℝ and prove that there exists a unique solution $u ∈ BUC(ℝ;L_{3,∞}(D))$ 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.
LA - eng
KW - Navier-Stokes flow; rotating obstacles
UR - http://eudml.org/doc/282523
ER -

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