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In this work we study the evolution of the interface between two differentfluids in two concentric cylinders when the velocity is given by theNavier-Stokes equation and one of the fluids is thin. We present a formalasymptotic derivation of the evolution equation for the interface underdifferent scaling assumptions for the surface tension. We then study thedifferent types of the stationary solutions and travelling waves for theresulting equation. In particular, we state a global well posedness result andusing Center Manifold Theory, we obtain detailed information about the longtime asymptotics of the solutions of the problem.

Analysis of a thin film approximation for two-fluid Taylord-Couette flows