TITLE: WELL-POSEDNESS OF THE FREE-SURFACE INCOMPRESSIBLE
EULER EQUATIONS WITH OR WITHOUT SURFACE TENSION

ABSTRACT: I'll describe a new methodology for treating free boundary
problems in me-
chanics, and use it to prove local-in-time well-posedness in Sobolev
spaces for the free-
surface incompressible 3D Euler equations with or without surface
tension for arbitrary
initial data, and without any irrotationality assumption on the fluid.
This is a free
boundary problem for the motion of an incompressible perfect liquid in
vacuum, wherein
the motion of the fluid interacts with the motion of the free-surface
at highest-order.