  In this work we study the evolution of the interface between two different
fluids in two concentric cylinders when the velocity is given by the
Navier-Stokes equation and one of the fluids is thin. We present a formal
asymptotic derivation of the evolution equation for the interface under
different scaling assumptions for the surface tension. We then study the
different types of the stationary solutions and travelling waves for the
resulting equation. In particular, we state a global well posedness result and
using Center Manifold Theory, we obtain detailed information about the long
time asymptotics of the solutions of the problem.
