Weak Solutions to a Fluid-Structure Interaction Model of a Viscous Fluid with an Elastic Plate under Coulomb Friction Coupling

We consider the behavior of a viscous fluid within a container that has an elastic upper, free boundary. The movement of the upper boundary is described by a combination of a plate equation and a boundary condition of friction type that quantifies the elasticity of the boundary. We show the local existence of weak solutions to this coupled system in three dimensions, by applying the Galerkin method to a regularized version of the problem and using a fixed-point argument afterwards.