Almost periodic motions and their stability of the non-autonomous Oseen–Navier–Stokes flows

In this paper, we investigate the existence and stability of almost periodic mild solutions to the non-autonomous Oseen–Navier–Stokes equations (ONSE) in the exterior domain \(\Omega \subset \mathbb {R}^3\) of a rigid body under the actions of almost periodic external forces. Our method is based on the \(L^p-L^q\) smoothness of the evolution family corresponding to linearized equations in combination with interpolation spaces and fixed point theorems.