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

• Autorzy: Toshiaki Hishida
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 76D05: Navier-Stokes equations
• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 86
• Numer: 1
• Strony: 149-162

Daty

wydano

2009

Twórcy

autor

Toshiaki Hishida

• Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

Identyfikatory

DOI

10.4064/bc86-0-9