Strong time-periodic solutions for a multilayered fluid-structure interaction system with nonlinear coupling
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arXiv
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| Format: | Preprint |
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2025
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| author | Brandt, Felix Mîndrilă, Claudiu Roy, Arnab |
| author_facet | Brandt, Felix Mîndrilă, Claudiu Roy, Arnab |
| contents | We investigate a time-periodic fully three-dimensional fluid-structure interaction system in which the Navier-Stokes equations for an incompressible viscous fluid are coupled with a multilayered elastic structure composed of a damped thin linear plate and a thick viscoelastic layer. The coupling is nonlinear, meaning that it is on a moving interface that is not known a priori, rendering the problem a moving-domain problem. We prove the existence of strong time-periodic solutions. The proof relies on a fixed point argument, combining sharp nonlinear estimates with a detailed analysis of the linearized system. The linearized problem is analyzed by employing the Arendt-Bu theorem on maximal periodic $\mathrm{L}^p$-regularity, which requires several new analytical ingredients including a refined lifting procedure, a decoupling strategy establishing $\mathcal{R}$-sectoriality of the coupled operator, a careful treatment of the thick structural layer, and a spectral analysis adapted to the multilayered setting. This provides the first strong time-periodic existence result for multilayered fluid-structure interaction systems, and the methods are expended to extend more broadly to nonlinear coupled PDEs on moving domains with periodic forcing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07918 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong time-periodic solutions for a multilayered fluid-structure interaction system with nonlinear coupling Brandt, Felix Mîndrilă, Claudiu Roy, Arnab Analysis of PDEs 74F10, 35R35, 35B10, 35Q30, 74H20, 35K59 We investigate a time-periodic fully three-dimensional fluid-structure interaction system in which the Navier-Stokes equations for an incompressible viscous fluid are coupled with a multilayered elastic structure composed of a damped thin linear plate and a thick viscoelastic layer. The coupling is nonlinear, meaning that it is on a moving interface that is not known a priori, rendering the problem a moving-domain problem. We prove the existence of strong time-periodic solutions. The proof relies on a fixed point argument, combining sharp nonlinear estimates with a detailed analysis of the linearized system. The linearized problem is analyzed by employing the Arendt-Bu theorem on maximal periodic $\mathrm{L}^p$-regularity, which requires several new analytical ingredients including a refined lifting procedure, a decoupling strategy establishing $\mathcal{R}$-sectoriality of the coupled operator, a careful treatment of the thick structural layer, and a spectral analysis adapted to the multilayered setting. This provides the first strong time-periodic existence result for multilayered fluid-structure interaction systems, and the methods are expended to extend more broadly to nonlinear coupled PDEs on moving domains with periodic forcing. |
| title | Strong time-periodic solutions for a multilayered fluid-structure interaction system with nonlinear coupling |
| topic | Analysis of PDEs 74F10, 35R35, 35B10, 35Q30, 74H20, 35K59 |
| url | https://arxiv.org/abs/2507.07918 |