Attainability of time-periodic flow of a viscous liquid past an oscillating body

Abstract

A body \(\mathscr {B}\) is started from rest by a translational motion in an otherwise quiescent Navier–Stokes liquid filling the whole space. We show, for small data, that if after some time \(\mathscr {B}\) reaches a spinless oscillatory motion of period \(\mathcal T\), the liquid will eventually execute also a time periodic motion with the same period \(\mathcal T\). This result is a suitable generalization of the famous Finn’s starting problem for steady states, to the case of time-periodic motions.

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Correspondence to Giovanni P. Galdi.

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G. P. Galdi: Partially supported by NSF Grant DMS-1614011.

T. Hishida: Partially supported by the Grant-in-Aid for Scientific Research 18K03363 from JSPS.

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Galdi, G.P., Hishida, T. Attainability of time-periodic flow of a viscous liquid past an oscillating body. J. Evol. Equ. (2021). https://doi.org/10.1007/s00028-020-00661-3

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