Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

The steady state Navier–Stokes equations for incompressible flows with rotating boundaries

Niko Sauera1

a1 Faculty of Science, University of Pretoria, Pretoria 0002, South Africa

Synopsis

When a rigid body performs a rotation in a fluid, the system of governing equations consists of conservation of linear momentum of the fluid and conservation of angular momentum of the rigid body. Since the torque at the interface involves the drag due to the fluid flow, the conservation of angular momentum may be viewed as a boundary condition for the field equations of fluid motion. The familiar no-slip condition becomes an additional equation in the system which not only governs the fluid motion, but also the motion of the rigid body. The unknown functions in the system of equations are the velocity field and the pressure field of the fluid motion and the angular velocity of the rigid body.

In this paper we obtain existence and uniqueness results for the steady state problem in which a rigid body rotates about an axis of symmetry in a viscous incompressible fluid.

(Received September 15 1987)

(Revised February 04 1988)