Periodic solutions to the non-autonomous Oseen-Navier-Stokes equations in exterior domains

Abstract

In this paper, we investigate the existence and uniqueness of periodic mild solutions to the non-autonomous Oseen-Navier-Stokes equations (ONSE) in the exterior domain of a rotating obstacle that is translating with a time-dependent velocity. Our method is based on the smoothness of the evolution family corresponding to linearized equations in combination with interpolation spaces and fixed-point theorems. Keywords: Evolution families, Periodic solutions, Oseen-Navier-Stokes equations, rotating and translating obstacle.