We study stability of a steady solution of the mathematical model describing the flow of a viscous incompressible fluid past a rotating body. We derive a sufficient condition for stability, which requires the L1 and L2–integrability on the time interval (0,\infty) of the semigroup generated by the relevant linear operator, applied to a finite family of suitable functions, in a norm restricted to a “sufficiently large” bounded region around the body. No assumption on the smallness of the steady solution is required.