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Publication 16-CNA-030
Yan Guo Ian Tice Abstract: In an effort to study the stability of contact lines in
fluids, we consider the dynamics of an
incompressible viscous Stokes
fluid evolving in a two-dimensional open-top vessel under the in
influence of
gravity. This is a free boundary problem: the interface between the
fluid in the vessel and the air above
(modeled by a trivial
fluid) is free to move and experiences capillary forces. The three-phase interface where
the
fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free
interface and the vessel is called the contact angle. We consider a model of this problem that allows for fully
dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then
allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that
decay to equilibrium exponentially fast.Get the paper in its entirety as 16-CNA-030.pdf |