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Author: Eiter, Thomas × DDC: 510 × Type: article × Subject: Time-periodic solutions ×

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    On the Stokes-Type Resolvent Problem Associated with Time-Periodic Flow Around a Rotating Obstacle
    (Dordrecht [u.a.] : Springer Science + Business Media B.V, 2022) Eiter, Thomas
    Consider the resolvent problem associated with the linearized viscous flow around a rotating body. Within a setting of classical Sobolev spaces, this problem is not well posed on the whole imaginary axis. Therefore, a framework of homogeneous Sobolev spaces is introduced where existence of a unique solution can be guaranteed for every purely imaginary resolvent parameter. For this purpose, the problem is reduced to an auxiliary problem, which is studied by means of Fourier analytic tools in a group setting. In the end, uniform resolvent estimates can be derived, which lead to the existence of solutions to the associated time-periodic linear problem.
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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.