- Published 2005

We develop a new methodology for treating free boundary problems in mechanics, and use it to prove local-in-time well-posedness in Sobolev spaces for the freesurface 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.

@inproceedings{Coutand2005WellposednessOT,
title={Well-posedness of the Free-surface Incompressible Euler Equations with or without Surface Tension},
author={Daniel Coutand and Steve Shkoller},
year={2005}
}