On Time-Periodic Bifurcation of a Sphere Moving under Gravity in a Navier-Stokes Liquid

Giovanni P. Galdi
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Giovanni P. Galdi: Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15260, USA

Mathematics, 2021, vol. 9, issue 7, 1-29

Abstract: We provide sufficient conditions for the occurrence of time-periodic Hopf bifurcation for the coupled system constituted by a rigid sphere, S , freely moving under gravity in a Navier-Stokes liquid. Since the region of flow is unbounded (namely, the whole space outside S ), the main difficulty consists in finding the appropriate functional setting where general theory may apply. In this regard, we are able to show that the problem can be formulated as a suitable system of coupled operator equations in Banach spaces, where the relevant operators are Fredholm of index 0. In such a way, we can use the theory recently introduced by the author and give sufficient conditions for time-periodic bifurcation to take place.

Keywords: fluid-structure interaction; Navier-Stokes equations; Hopf bifurcation; falling sphere (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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