8. Stochastic FSI: A Fully Coupled Model with Linear Coupling

This chapter delves into the study of stochastic fluid-structure interaction (FSI) with a focus on developing a fully coupled model with linear coupling. The text begins by reviewing a reduced model from a previous chapter and highlights the limitations of unbounded geometries in real-life applications. The author then introduces a more general framework for analyzing stochastic FSI models on bounded domains, utilizing an operator splitting method to construct random approximate solutions. The model considers a stochastically perturbed 2D linear Stokes flow interacting with a stochastically forced 1D elastic membrane, described by a Koiter shell equation. The chapter discusses the notion of weak solutions and presents a constructive approach to study these solutions, emphasizing the use of Fourier analysis and fundamental solutions. The author derives a priori energy estimates and discusses the splitting scheme, which involves structure and fluid subproblems. The chapter concludes with a discussion on passing to the limit in the approximate solutions and the existence of weak martingale solutions. This comprehensive analysis provides valuable insights into the behavior of stochastic FSI systems and offers a robust framework for future research in this area.