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arXiv · 2507.07918

Strong time-periodic solutions for a multilayered fluid-structure interaction system with nonlinear coupling

Felix Brandt·Claudiu Mîndrilă·Arnab Roy
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Abstract

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.

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Felix Brandt, Claudiu Mîndrilă, Arnab Roy. 2025-07-10. Strong time-periodic solutions for a multilayered fluid-structure interaction system with nonlinear coupling. https://doi.org/10.1088/1361-6544%2Fae5203

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