Existence and uniqueness for a quasi-static interaction problem between a viscous fluid and an active structure

We consider a quasi-static fluid-structure interaction problem where the fluid is modeled by theStokes equations and the structure is an active and elastic medium. More precisely, the displacementof the structure verifies the equations of elasticity with an active stress, which models the presenceof internal biological motors in the structure. Under smallness assumptions on the data, we provethe existence of a unique solution for this strongly coupled system.