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

Giovanni P. Galdi

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arXiv · 2102.13134

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

Giovanni P. Galdi

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Abstract

We provide sufficient conditions for the occurrence of time-periodic Hopf bifurcation for the coupled system constituted by a rigid sphere, $\mathscr S$, freely moving under gravity in a Navier-Stokes liquid. Since the region of flow is unbounded (namely, the whole space outside $\mathscr S$), 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.

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BibTeX RIS

Giovanni P. Galdi. 2021-02-25. On Time-Periodic Bifurcation of a Sphere Moving under Gravity in a Navier-Stokes Liquid. https://arxiv.org/abs/2102.13134

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