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 the 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
Citation
Thomas EITER. Yoshihiro SHIBATA. "Viscous flow past a translating body with oscillating boundary." J. Math. Soc. Japan 77 (1) 103 - 134, January, 2025. https://doi.org/10.2969/jmsj/91649164
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