Special Colloquium
David Ambrose
Clemson University
Free Surface Problems in Fluid Dynamics
Abstract: Fluid flows in the presence of free surfaces occur in a great
many situations in nature; examples include waves on the ocean
and the flow of groundwater. In this talk, I will discuss my
contributions to the analysis of the systems of nonlinear
partial differential equations which model such phenomena.
In particular, I will discuss short-time well-posedness theorems
for three particular free surface problems: vortex sheets with
surface tension, water waves, and interfacial flows in porous
media. Each of these problems is considered in both two and
three space dimensions; some of these results are from joint
work with Nader Masmoudi. The main ingredients in the proofs are
a reformulation of the evolution equations using a convenient
parameterization of the free surface, and approximations of
singular integrals using Hilbert or Riesz transforms. With the
well-posedness of the problems established for short times, many
questions remain about the long-time behavior. To address one
such question, I will present numerical evidence of formation of
isolated curvature singularites for the two-dimensional vortex
sheet with surface tension.
There will be coffee, tea and cookies in SEO 300 from 4:00 to 4:30. Stop by to meet David Ambrose
Wednesday December 5, 2007 at 3:00 PM in SEO 636