On periodic motions of a harmonic oscillator interacting with incompressible fluids

We consider a mass–spring system immersed in an incompressible fluid flow governed by the Navier–Stokes equations subject to a prescribed time-periodic flow rate (and possibly external time-periodic body forces on the fluid and the mass). We show that, with no restriction on the period of the flow r...

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Bibliographic Details
Published inPhysica. D Vol. 467; p. 134259
Main Authors Mazzone, Giusy, Mohebbi, Mahdi
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2024
Subjects
Navier–Stokes equations
Periodic solutions
Resonance
Undamped mass–spring-fluid interaction
Navier–Stokes equations
35D35
Periodic solutions
35B34
74F10
35D30
35B10
76D05
Resonance
35Q30
Undamped mass–spring-fluid interaction
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Summary:We consider a mass–spring system immersed in an incompressible fluid flow governed by the Navier–Stokes equations subject to a prescribed time-periodic flow rate (and possibly external time-periodic body forces on the fluid and the mass). We show that, with no restriction on the period of the flow rate (and of the external forces), when the flow rate is “small”, there exists a weak time-periodic solution to the coupled system. Under some more regularity and “smallness” conditions on the flow rate (and the external forces) we also show that these solutions are, indeed, strong solutions. •Existence of periodic solutions to a partially dissipative system.•Periodic motion of an undamped harmonic oscillator in a Navier–Stokes fluid.•Fluid damping in fluid–solid interactions.
ISSN:0167-2789
DOI:10.1016/j.physd.2024.134259