On finite-time contact in a fluid-elastic structure interaction problem

Krutika Tawri, University of Washington
9/23, 2026 at 11:10AM-12:00PM in 939 Evans (for in-person talks) and https://berkeley.zoom.us/j/98667278310

Abstract: In this talk, we will consider a fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the 2D Navier-Stokes equations, through a thin deformable elastic tube, elastodynamics of which is modeled by 1D plate equations. The fluid and the structure are nonlinearly coupled at the fluid-structure interface. The fluid flow is driven by Bernoulli pressure data imposed at the inlet and the outlet of the tube. In this talk, we will impose the Navier-slip boundary condition at the fluid-structure interface and at the bottom rigid boundary of the fluid domain. We will first discuss the existence of weak solutions and reveal a `hidden' spatial regularity result for the structure displacement. We then present our recent result identifying conditions under which a weak solution reaches a finite time at which the compliant upper boundary meets the lower boundary, causing the elastic channel to collapse. This result resolves the “no-collision” paradox previously identified in the no-slip setting and thus validates the model to correctly capture near-contact dynamics.