  In this paper, we prove the local well-posedness of the free boundary problem
for the incompressible Euler equations in low regularity Sobolev spaces, in
which the velocity is a Lipschtiz function and the free surface belongs to
$C^{\f32+\varepsilon}$. Moreover, we also present a Beale-Kato-Majda type
break-down criterion of smooth solution in terms of the mean curvature of the
free surface, the gradient of the velocity and Taylor sign condition.
