Publication 16-CNA-032
Dynamics And Stability Of Surface Waves With Surfactants
Chanwoo Kim
Department of Mathematics
University of Wisconsin
Madison, Madison, WI 53706 USA
chanwoo.kim@wisc.edu
Ian Tice
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
ian.tice@andrew.cmu.edu
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.
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