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search.filters.applied.f.access: openAccess × Author: Eiter, Thomas × End date: 2022 × Start date: 2021 × Type: Text × Subject: Oseen flow ×

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    Viscous Flow Around a Rigid Body Performing a Time-periodic Motion
    (Cham (ZG) : Springer International Publishing AG, 2021) Eiter, Thomas; Kyed, Mads
    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.
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    On the Oseen-type resolvent problem associated with time-periodic flow past a rotating body
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Eiter, Thomas
    Consider the time-periodic flow of an incompressible viscous fluid past a body performing a rigid motion with non-zero translational and rotational velocity. We introduce a framework of homogeneous Sobolev spaces that renders the resolvent problem of the associated linear problem well posed on the whole imaginary axis. In contrast to the cases without translation or rotation, the resolvent estimates are merely uniform under additional restrictions, and the existence of time-periodic solutions depends on the ratio of the rotational velocity of the body motion to the angular velocity associated with the time period. Provided that this ratio is a rational number, time-periodic solutions to both the linear and, under suitable smallness conditions, the nonlinear problem can be established. If this ratio is irrational, a counterexample shows that in a special case there is no uniform resolvent estimate and solutions to the time-periodic linear problem do not exist.