Viscous flow around a rigid body performing a time-periodic motion

Thomas Eiter; Mads Kyed

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arXiv · 1912.04938

Viscous flow around a rigid body performing a time-periodic motion

Thomas Eiter·Mads Kyed

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Abstract

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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Thomas Eiter, Mads Kyed. 2019-12-10. Viscous flow around a rigid body performing a time-periodic motion. https://arxiv.org/abs/1912.04938

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