1. Stability of equilibria and bifurcations for a fluid-solid interaction problem.
- Author
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Bonheure, Denis, Galdi, Giovanni P., and Gazzola, Filippo
- Subjects
- *
NAVIER-Stokes equations , *EQUILIBRIUM , *VELOCITY , *FLUIDS , *LIQUIDS - Abstract
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 ≥ λ c. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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