  We are interested by the controllability of a fluid-structure interaction
system where the fluid is viscous and incompressible and where the structure is
elastic and located on a part of the boundary of the fluid's domain. In this
article, we simplify this system by considering a linearization and by
replacing the wave/plate equation for the structure by a heat equation. We show
that the corresponding system coupling the Stokes equations with a heat
equation at its boundary is null-controllable. The proof is based on Carleman
estimates and interpolation inequalities. One of the Carleman estimates
corresponds to the case of Ventcel boundary conditions. This work can be seen
as a first step to handle the real system where the structure is modeled by the
wave or the plate equation.
