David Ambrose
Department of Mathematical Sciences
Clemson University

In this talk, I will describe my proofs of short-time well-posedness of various free surface problems in irrotational 3D fluids. The method has been used to prove well-posedness of vortex sheets with surface tension, water waves, and Darcy flows. I will describe a common framework for treating each of these problems: this involves making an isothermal parameterization of the free surface and choosing convenient dependent variables. Energy estimates can then be performed, and these estimates lead to well-posedness. The case of Darcy flow will be discussed in detail. Some of this work is joint with Nader Masmoudi.