Finite energy weak solutions to a multilayered 3D fluid-poroelastic structure interaction problem

In this talk, we discuss the existence of a finite energy weak solution to a nonlinearly coupled multilayered 3D fluid-poroelastic structure interaction problem. At the top, we consider a thick poroelastic Biot model, which is separated from the incompressible viscous fluid by a thin reticular plate. The latter acts as a moving interface with mass between the two thick layers. The model is complemented by suitable kinematic coupling conditions, including the Beavers-Joseph-Saffman conditions for tangential slip, and dynamic coupling conditions. The existence of a finite energy weak solution to a regularized version of the model is obtained by means of semidiscretization and a splitting scheme. The lack of Lipschitz regularity of the fluid domain poses significant challenges when establishing weak and weak* convergences of the sequence of approximate solutions. The upgrade to strong convergence for the limit passage in the nonlinear problem involves compactness results due to Dreher and Jüngel as well as a generalized Aubin-Lions compactness criterion for moving domains. The talk is based on joint work (work in progress) with S. Čanić (UC Berkeley) and B. Muha (University of Zagreb).