Existence for a Quasi-Static Interaction Problem Between a Viscous Fluid and an Active Structure

Abstract

We consider a quasi-static fluid–structure interaction problem where the fluid is modeled by the Stokes equations and the structure is an active elastic material. More precisely, the displacement of the structure satisfies the equations of elasticity with an additional active stress, which models the presence of internal biological motors in the structure. Under smallness assumptions on the data, we prove the existence of a solution for this strongly coupled system.