On the finite-time splash singularity for the 3-D free-surface Euler equations

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'' singularity, wherein the evolving 2-D hypersurface intersects itself at a point. Our approach is based on the Lagrangian description of the free-boundary problem, combined with novel approximation scheme. We do not assume the fluid is irrotational, and as such, our method can be used for a number of other fluid interface problems. This is joint work with Daniel Coutand.