  We consider a coupled two-phase Navier-Stokes/Mullins-Sekerka system
describing the motion of two immiscible, incompressible fluids inside a bounded
container. The moving interface separating the liquids meets the boundary of
the container at a constant ninety degree angle. This common interface is
unknown and has to be determined as a part of the problem.
  We show well-posedness and investigate the long-time behaviour of solutions
starting close to certain equilibria. We prove that for equal densities these
solutions exist globally in time, are stable, and converge to an equilibrium
solution at an exponential rate.
