Equilibrium configurations of a 3D fluid-beam interaction problem
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908794982760448 |
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| author | Bianca, Vincenzo Bocchi, Edoardo Gazzola, Filippo |
| author_facet | Bianca, Vincenzo Bocchi, Edoardo Gazzola, Filippo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equilibrium configurations of a 3D fluid-beam interaction problem Bianca, Vincenzo Bocchi, Edoardo Gazzola, Filippo Analysis of PDEs 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. |
| title | Equilibrium configurations of a 3D fluid-beam interaction problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.10523 |