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

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Hishida T.

Banach Center Publications

2009

tom 86

nr 1

149-162

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.

Ograniczanie wyników

1 Banach Center Publications

1 Hishida T.

1 2009

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