STEVE SHKOLLER
Department of Mathematics
University of California at Davis
Davis, CA 95616, USA
http://www.math.ucdavis.edu/
shkoller@math.ucdavis.edu
Abstract:
We model the cusp formation on the boundary of an air bubble rising inside a
complex (non-Newtonian) fluid such as a liquid crystal. We derive a
model in which the surface tension of the bubble competes with molecular
alignment forces of the complex fluid and eventually loses. The problem
requires modeling the interface of the bubble, and we use level set
methods which are coupled with the and Ericksen-Leslie model for liquid
crystals. After discussing the model, we shall present a simple proof of
global-wellposedness of the Ericksen-Leslie liquid crystal model on
a Riemannian manifold.