On a Stochastic Moving Boundary Fluid-Structure Interaction Problem

In this talk, we will investigate the existence of martingale solutions to a nonlinearly coupled fluid-structure interaction problem involving an incompressible, viscous fluid flow and a deformable structure subjected to a multiplicative stochastic force. The fluid flow is described by the Navier-Stokes equations while the elastodynamics of the thin structure is modeled by membrane/shell equations. We will introduce a constructive method based on a Lie operator splitting scheme and a cut-off function approach. We will discuss the challenges that arise due to the unrestricted random motion of the time-dependent fluid domain and present our recent findings.