Stability of equilibria and bifurcations for a fluid-solid interaction problem
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911908632723456 |
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| author | Bonheure, Denis Galdi, Giovanni P. Gazzola, Filippo |
| author_facet | Bonheure, Denis Galdi, Giovanni P. Gazzola, Filippo |
| contents | We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is driven by a uniform flow at spatial infinity, with constant dimensionless velocity $λ$. We show that if $λ$ is below a critical value, $λ_c$ (say), there is a unique and stable time-independent configuration, where the body is in equilibrium and the flow is steady. We also prove that, if $λ<λ_c$, no oscillatory flow may occur. Successively, we investigate possible loss of uniqueness by providing necessary and sufficient conditions for the occurrence of a steady bifurcation at some $λ_s\ge λ_c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of equilibria and bifurcations for a fluid-solid interaction problem Bonheure, Denis Galdi, Giovanni P. Gazzola, Filippo Analysis of PDEs 76D05, 74F10, 35B32, 76D03 We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is driven by a uniform flow at spatial infinity, with constant dimensionless velocity $λ$. We show that if $λ$ is below a critical value, $λ_c$ (say), there is a unique and stable time-independent configuration, where the body is in equilibrium and the flow is steady. We also prove that, if $λ<λ_c$, no oscillatory flow may occur. Successively, we investigate possible loss of uniqueness by providing necessary and sufficient conditions for the occurrence of a steady bifurcation at some $λ_s\ge λ_c$. |
| title | Stability of equilibria and bifurcations for a fluid-solid interaction problem |
| topic | Analysis of PDEs 76D05, 74F10, 35B32, 76D03 |
| url | https://arxiv.org/abs/2406.04162 |