  We prove that the 3-D free-surface incompressible Euler equations with
regular initial geometries and velocity fields have solutions which can form a
finite-time "splash" (or "splat") singularity first introduced in [9], wherein
the evolving 2-D hypersurface, the moving boundary of the fluid domain,
self-intersects at a point (or on surface). Such singularities can occur when
the crest of a breaking wave falls unto its trough, or in the study of drop
impact upon liquid surfaces. Our approach is founded upon the Lagrangian
description of the free-boundary problem, combined with a novel approximation
scheme of a finite collection of local coordinate charts; as such we are able
to analyze a rather general set of geometries for the evolving 2-D free-surface
of the fluid. We do not assume the fluid is irrotational, and as such, our
method can be used for a number of other fluid interface problems, including
compressible flows, plasmas, as well as the inclusion of surface tension
effects.
