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Publication 16-CNA-032
Chanwoo Kim Ian Tice Abstract: In this paper we consider a layer of incompressible viscous
fluid lying above a
at periodic surface
in a uniform gravitational field. The upper boundary of the
fluid is free and evolves in time. We assume
that a mass of surfactants resides on the free surface and evolves in time with the
fluid. The surfactants
dynamics couple to the
fluid dynamics by adjusting the surface tension coefficient on the interface and also
through tangential Marangoni stresses caused by gradients in surfactant concentration. We prove that small
perturbations of equilibria give rise to global-in-time solutions in an appropriate functional space, and we
prove that the solutions return to equilibrium exponentially fast. In particular this proves the asymptotic
stability of equilibria.Get the paper in its entirety as 16-CNA-032.pdf |