UW Analysis, Geometry and Dynamics Seminar: Krutika Tawri

In this talk we will discuss recent results concerning stochastic (and deterministic) free boundary problems, particularly arising in fluid structure interaction (FSI). We will begin by considering a nonlinearly coupled FSI system perturbed by stochastic effects involving a viscous fluid modeled by the Navier-Stokes equations in a 2D/3D domain, where part of the fluid domain boundary consists of an elastic deformable structure modeled by plate equations. The fluid and the structure are coupled via two sets of coupling conditions (balance of stress and kinematic entities) imposed at the fluid-structure interface. We will present results for both incompressible and compressible fluid flows. We will also discuss various kinematic coupling conditions and their implications for degeneracies in the problem. Finally, we will discuss long-time behavior of the solutions to a reduced stochastic FSI model obtained by spatially averaging a component of the fluid velocity in long compliant tubes.