Eiter, Thomas; Kyed, Mads Viscous flow around a rigid body performing a time-periodic motion. (English) Zbl 1460.35255 J. Math. Fluid Mech. 23, No. 1, Paper No. 28, 24 p. (2021). Summary: The 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. Cited in 5 Documents MSC: 35Q30 Navier-Stokes equations 35B10 Periodic solutions to PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids 76D07 Stokes and related (Oseen, etc.) flows 76U05 General theory of rotating fluids 41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) Keywords:Navier-Stokes; Oseen flow; time-periodic solutions; rotating obstacles PDFBibTeX XMLCite \textit{T. Eiter} and \textit{M. Kyed}, J. Math. Fluid Mech. 23, No. 1, Paper No. 28, 24 p. (2021; Zbl 1460.35255) Full Text: DOI arXiv References: [1] Bruhat, F., Distributions sur un groupe localement compact et applications à l’étude des représentations des groupes \(p\)-adiques, Bull. Soc. Math. Fr., 89, 43-75 (1961) · Zbl 0128.35701 [2] Burenkov, V. I.: Extension of functions with preservation of the Sobolev seminorm. Trudy Mat. Inst. Steklov., 172:71-85, 1985. (English transl.: Proc. Steklov Inst. 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