Stochastic moving boundary problems arising in fluid-dynamics
and long-time behavior of the solutions 

The aim of this talk is twofold: 1. We will first investigate the existence of weak solutions to a benchmark fluid-structure interaction problem,
that involves a viscous fluid interacting with an elastic membrane, perturbed
with white-in-time stochastic forces. The fluid flow is described by the Navier-
Stokes equations while the elastodynamics of the thin structure is modeled by
the plate equations. The fluid and the structure are coupled via two sets of
coupling conditions imposed at the fluid-structure interface.
2. We will then consider a simplified version of this model, which reduces to
a system structurally analogous to the stochastic compressible Euler equations
with linear damping. For this reduced system, we will discuss the long-time
dynamics and, in particular, the existence of statistically stationary solutions
by means of constructing approximations that preserve key Euler structures
while admitting invariant dynamics, and extracting uniform estimates from the
limited dissipation provided by the linear damping.