Viscous flow past a translating body with oscillating boundary

Thomas Eiter; Yoshihiro Shibata

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arXiv · 2303.09592

Viscous flow past a translating body with oscillating boundary

Thomas Eiter·Yoshihiro Shibata

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Abstract

We study an incompressible viscous flow around an obstacle with an oscillating boundary that moves by a translational periodic motion, and we show existence of strong time-periodic solutions for small data in different configurations: If the mean velocity of the body is zero, existence of time-periodic solutions is provided within a framework of Sobolev functions with isotropic pointwise decay. If the mean velocity is non-zero, this framework can be adapted, but the spatial behavior of flow requires a setting of anisotropically weighted spaces. In the latter case, we also establish existence of solutions within an alternative framework of homogeneous Sobolev spaces. These results are based on the time-periodic maximal regularity of the associated linearizations, which is derived from suitable R-bounds for the Stokes and Oseen resolvent problems. The pointwise estimates are deduced from the associated time-periodic fundamental solutions.

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Thomas Eiter, Yoshihiro Shibata. 2023-03-16. Viscous flow past a translating body with oscillating boundary. https://arxiv.org/abs/2303.09592

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