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Funkcialaj Ekvacioj
Vol. 50 (2007) No. 3 P 371-403



Consider a viscous incompressible fluid filling the whole 3-dimensional space exterior to a rotating body with constant angular velocity ω. By using a coordinate system attached to the body, the problem is reduced to an equivalent one in a fixed exterior domain. The reduced equation involves the crucial drift operator (ω ∧ x) · ∇, which is not subordinate to the usual Stokes operator. This paper addresses stationary flows to the reduced problem with an external force f = div F, that is, time-periodic flows to the original one. Generalizing previous results of G. P. Galdi [19] we show the existence of a unique solution (∇u, p) in the class L3/2,∞ when both FL3/2,∞ and ω are small enough; here L3/2,∞ is the weak-L3/2 space.

Copyright © 2007 by the Division of Functional Equations, The Mathematical Society of Japan

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