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

This talk addresses a nonlinear time-periodic fluid-structure interaction problem in which the Navier-Stokes equations for an incompressible viscous fluid are coupled with a multilayered elastic structure composed of a damped thin shell and a thick viscoelastic layer. We discuss 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 L^p-regularity, which requires several new analytical ingredients including a refined lifting procedure, a decoupling strategy establishing R-sectoriality of the coupled operator, a careful treatment of the thick structural layer, and a spectral analysis adapted to the multilayered setting.  The talk is based on joint work with Claudiu Mindrila and Arnab Roy.