10. FPSI with Linear Coupling

This chapter examines a linearly coupled fluid-poroelastic structure interaction (FPSI) system, focusing on the existence of weak solutions. The study considers an incompressible, viscous fluid modeled by the time-dependent Stokes equations interacting with a multilayered poroelastic structure, which includes a thin poroelastic plate and a thick Biot poroelastic material. The chapter presents the mathematical formulation of the system, detailing the spatial domain and the governing equations for each sub-region. It also discusses the coupling conditions between the fluid and the poroelastic structure, including kinematic and dynamic coupling conditions. The chapter provides a formal energy estimate and defines the function spaces for weak solutions. It then presents the weak formulation of the problem and proves the existence of weak solutions using Rothe's method and energy estimates. The chapter also addresses the uniqueness of solutions and discusses the quasi-static nonlinear problem, providing a comprehensive analysis of the FPSI system.