Special colloquium: International Day of Women in Mathematics

Barbora Benesova (Charles-University, Prague)

A variational approach to fluid structure interaction

In this talk we will consider the interaction of a Stokes/Navier-Stokes flow with a viscoelastic body. The elastic body is allowed to undergo large de- formations (but no self-collisions). In order to handle this situation correctly, we devise a variational approximation scheme in the spirit of De Giorgi to the combined problem. Moreover, by using a two-scale scheme, we also extend this approach to the hyperbolic regime including inertia of the solid body.

These variational approaches allow us to prove proper energetic estimates while also controlling the geometric restrictions posed on the solid body and, eventually, to establish existence of weak solutions. This is a joint work with Malte Kamp- schulte (Charles University) and Sebastian Schwarzacher (University of Uppsala & Charles University).