CC BY 4.0 UnportedEiter, ThomasKyed, Mads2022-03-232022-03-232021https://oa.tib.eu/renate/handle/123456789/8321https://doi.org/10.34657/7359The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and the angular velocity of the prescribed rigid-body motion are compatible, and that the mean translational velocity is non-zero, existence of a time-periodic solution is established. The proof is based on an appropriate linearization, which is examined within a setting of absolutely convergent Fourier series. Since the corresponding resolvent problem is ill-posed in classical Sobolev spaces, a linear theory is developed in a framework of homogeneous Sobolev spaces.enghttps://creativecommons.org/licenses/by/4.0/510Navier-StokesOseen flowRotating obstaclesTime-periodic solutionsArticle