Steady weak solutions to an inflow/outflow driven compressible fluid-structure interaction problem
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910078480678912 |
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| author | Muha, Boris Nečasová, Šárka Pokorný, Milan Trifunović, Srđan Webster, Justin T. |
| author_facet | Muha, Boris Nečasová, Šárka Pokorný, Milan Trifunović, Srđan Webster, Justin T. |
| contents | We study a stationary 3D/2D fluid-structure interaction problem between an elastic structure described by the linear plate equation and a fluid described by the compressible Navier-Stokes equations with hard-sphere pressure and inflow/outflow boundary data. This problem is motivated by wind-tunnel configuration and by the need for physically relevant steady states about which compressible flow-plate dynamics can be linearized.
The main difficulty in the analysis is the lack of uniform estimates, both for approximate and weak solutions. In particular, the fixed-point construction for approximate solution yields a density estimate depending on approximate parameter, while the pressure estimate for the weak solution is only finite and non-quantifiable. As a result, large pressure loads can drive outward volume growth, while low pressure regions may lead to contact and therefore domain degeneration. This necessitates a novel approach based on a Lipschitz \emph{domain-correction} (barrier) mechanism that provides a framework in which solutions can be constructed without volume blow-up or degeneration of the domain. Constrained by the possibly very large fluid pressure load, our main result is the existence of a weak solution for a sufficiently large plate stiffness.
Keywords: fluid-structure interaction, compressible Navier-Stokes, stationary weak solutions, hard-sphere pressure, inflow/outflow, linear plate, mathematical aeroelasticity |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26421 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Steady weak solutions to an inflow/outflow driven compressible fluid-structure interaction problem Muha, Boris Nečasová, Šárka Pokorný, Milan Trifunović, Srđan Webster, Justin T. Analysis of PDEs 74F10, 76N10, 35Q35, 35D30, 76N15, 74K20 We study a stationary 3D/2D fluid-structure interaction problem between an elastic structure described by the linear plate equation and a fluid described by the compressible Navier-Stokes equations with hard-sphere pressure and inflow/outflow boundary data. This problem is motivated by wind-tunnel configuration and by the need for physically relevant steady states about which compressible flow-plate dynamics can be linearized. The main difficulty in the analysis is the lack of uniform estimates, both for approximate and weak solutions. In particular, the fixed-point construction for approximate solution yields a density estimate depending on approximate parameter, while the pressure estimate for the weak solution is only finite and non-quantifiable. As a result, large pressure loads can drive outward volume growth, while low pressure regions may lead to contact and therefore domain degeneration. This necessitates a novel approach based on a Lipschitz \emph{domain-correction} (barrier) mechanism that provides a framework in which solutions can be constructed without volume blow-up or degeneration of the domain. Constrained by the possibly very large fluid pressure load, our main result is the existence of a weak solution for a sufficiently large plate stiffness. Keywords: fluid-structure interaction, compressible Navier-Stokes, stationary weak solutions, hard-sphere pressure, inflow/outflow, linear plate, mathematical aeroelasticity |
| title | Steady weak solutions to an inflow/outflow driven compressible fluid-structure interaction problem |
| topic | Analysis of PDEs 74F10, 76N10, 35Q35, 35D30, 76N15, 74K20 |
| url | https://arxiv.org/abs/2603.26421 |