Strong time-periodic solutions to a multilayered fluid-structure interaction problem

2025/07/10 by Brandt, Felix, Mîndrilă, Claudiu, Roy, Arnab · 1 citation
#35B10 #35K59 #35Q30 #35R35 #74F10 #74H20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.07918

Abstract

This article studies a nonlinearly coupled, time-periodic fluid-structure interaction (FSI) problem involving the Navier-Stokes equations for an incompressible, viscous fluid coupled with a multilayered elastic structure consisting of a thin damped shell and a thick viscoelastic component. The main objective is to establish the existence of a strong time-periodic solution. To address the full nonlinear problem, we employ a fixed point argument, which relies on a detailed analysis of the linearized system together with appropriate nonlinear estimates. The linearized problem is analyzed by employing the Arendt-Bu theorem on maximal periodic L^p-regularity, which requires several new analytical ingredients including a careful treatment of the thick structural layer, a refined lifting procedure, a decoupling strategy to establish R-sectoriality of the associated FSI operator and a careful spectral analysis. To the best of our knowledge, this is the first result proving the existence of strong time-periodic solutions for a multilayered fluid-structure interaction problem.

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