Spatial stability of 3D exterior stationary Navier-Stokes flows

In this paper, we study the stability of stationary solutions w for the Navier-Stokes flows in an exterior domain with zero velocity at infinity. With suitable assumptions of w, by the works of Chen (1993), Kozono-Ogawa (1994) and Borchers-Miyakawa (1995), if u0−w∈Lr(Ω)∩L3(Ω) then one can obtain‖u(t)−w‖p=O(t−32(1r−1p))for 13r3−rα.