Boeing Colloquium: Suncica Canic (UC Berkeley)

About this event

Title : Recent Mathematical Advances in Fluid–Structure Interaction Involving Elastic and Poroelastic Structures, Motivated by Biomedical Applications

Abstract : We will review recent mathematical advances in fluid–structure interaction (FSI) involving elastic and poroelastic structures. FSI problems arise whenever fluid motion and the deformation of an adjacent compliant structure (solid) influence one another and must therefore be determined simultaneously. Although the governing equations for the fluid and the structure have each been studied extensively, their coupled behavior remains less well understood because it presents major mathematical challenges: the fluid domain is itself unknown, evolves in time, and is determined by the motion of a structure whose deformation is also part of the solution. These challenges become particularly pronounced when the moving interface is rough—that is, when its displacement possesses only the limited spatial regularity furnished by the natural energy estimates.

In this talk, I will review recent results concerning the coupling of the Navier–Stokes equations for an incompressible viscous fluid with elastic, viscoelastic, and poroelastic structures through both linear and nonlinear geometric coupling. I will also discuss how these mathematical advances have informed the design of a second-generation bioartificial pancreas and a vascular stent developed to anchor a bioartificial heart valve.