Local well-posedness and break-down criterion of the incompressible Euler equations with free boundary

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