  We consider a coupled system of partial differential equations describing the
interactions between a closed free interface and two viscous incompressible
fluids. The fluids are assumed to satisfy the incompressible Navier-Stokes
equations in time-dependent domains that are determined by the free interface.
The mean curvature of the interface induces a surface tension force that
creates a jump of the Cauchy stress tensor on both sides. It influences the
behavior of the surrounding fluids, and therefore the deformation of this
interface via the equality of velocities. In dimension 2, the steady states
correspond to immobile interfaces that are circles with all the same volume.
Considering small displacements of steady states, we are lead to consider a
linearized version of this system. We prove that the latter is approximately
controllable to a given steady state for any time $T>0$ by the means of
additional surface tension type forces, provided that the radius of the circle
of reference does not coincide with a scaled zero of the Bessel function of
first kind.
