Analysis Seminar

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The stability of contact lines in fluids

Speaker: Ian TICE, Carnegie-Mellon University

Location: Warren Weaver Hall 1302

Date: Thursday, February 14, 2019, 11 a.m.

Synopsis:

The contact line problem in interfacial fluid mechanics concerns
the triple-junction between a fluid, a solid, and a vapor phase.
Although the equilibrium configurations of contact lines have been
well-understood since the work of Young, Laplace, and Gauss, the
understanding of contact line dynamics remains incomplete and is a
source of work in experimentation, modeling, and mathematical analysis.
In this talk we consider a 2D model of contact point (the 2D analog of a
contact line) dynamics for an incompressible, viscous, Stokes fluid
evolving in an open-top vessel in a gravitational field. The model
allows for fully dynamic contact angles and points. We show that small
perturbations of the equilibrium configuration give rise to
global-in-time solutions that decay to equilibrium exponentially fast.