On the existence of steady flows of a Navier–Stokes liquid around a moving rigid body

We prove the existence of a strong solution to the three‐dimensional steady Navier–Stokes equations in the exterior of an obstacle undergoing a rigid motion. Unlike the classical exterior problem for the Navier–Stokes equations, that only takes into account the translational motion of the obstacle, is this case, the obstacle can also rotate. Assuming the total flux of the velocity field through the boundary to be sufficiently small, we first construct approximating solutions in bounded regions Ω_R = Ω∩ {x ∈ ?³:∣x∣< R} invading the liquid domain Ω. A set of estimates independent of R are shown to hold for the approximating solutions which allows to obtain a strong solution by taking the limit R→∞. Copyright © 2004 John Wiley & Sons, Ltd.