Equilibrium configurations of a 3D fluid-beam interaction problem
Analysis of PDEs
2026-01-30 v3
Abstract
We study a fluid-structure interaction problem between a viscous incompressible fluid and an elastic beam with fixed endpoints in a static setting. The 3D fluid domain is bounded, nonsmooth and non simply connected, the fluid is modeled by the stationary Navier-Stokes equations subject to inflow/outflow conditions. The structure is modeled by a stationary 1D beam equation with a load density involving the force exerted by the fluid and, thereby, may vary its position. In a smallness regime, we prove the existence and uniqueness of the solution to the PDE-ODE coupled system.
Cite
@article{arxiv.2507.10523,
title = {Equilibrium configurations of a 3D fluid-beam interaction problem},
author = {Vincenzo Bianca and Edoardo Bocchi and Filippo Gazzola},
journal= {arXiv preprint arXiv:2507.10523},
year = {2026}
}
Comments
This version contains minor changes with respect to the published version in App. Math. Optim. 92, 50 (2025)