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

Abstract

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.