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

Banach Center Publications (2009)

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

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topToshiaki 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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