Stationary Navier-Stokes Flow Around a Rotating Obstacle

Abstract

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 [formula omitted], 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 FεL3/2,∞and ω are small enough; here L3/2,∞is the weak-L3/2space. © 2007, Division of Functional Equations, The Mathematical Society of Japan. All rights reserved.