January, 2025 Viscous flow past a translating body with oscillating boundary
Thomas EITER, Yoshihiro SHIBATA
Author Affiliations +
J. Math. Soc. Japan 77(1): 103-134 (January, 2025). DOI: 10.2969/jmsj/91649164

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 R-bounds for the Stokes and Oseen resolvent problems. The pointwise estimates are deduced from the associated time-periodic fundamental solutions.

Citation

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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

Information

Received: 3 July 2023; Published: January, 2025
First available in Project Euclid: 22 July 2024

Digital Object Identifier: 10.2969/jmsj/91649164

Subjects:
Primary: 76D05
Secondary: 35B10 , 35B40 , 35Q30 , 35R37 , 76D07

Keywords: exterior domain , maximal regularity , Moving boundary , spatial decay , time-periodic solutions

Rights: Copyright ©2025 Mathematical Society of Japan

Vol.77 • No. 1 • January, 2025
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