Attainability of a stationary Navier-Stokes flow around a rigid body rotating from rest

We consider the large time behavior of the three-dimensional Navier-Stokes flow around a rotating rigid body. Assume that the angular velocity of the body gradually increases until it reaches a small terminal one at a certain finite time and it is fixed afterwards. We then show that the fluid motion converges to a steady solution as time $t\to \mathrm{\infty }$.