A simple proof of well-posedness for the free-surface incompressible euler equations

Abstract

The purpose of this this paper is to present a new simple proof for the construction of unique solutions to the moving free-boundary incom-pressible 3-D Euler equations in vacuum. Our method relies on the Lagrangian representation of the fluid, and the anisotropic smoothing operation that we call horizontal convolution-by-layers. The method is general and can be ap-plied to a number of other moving free-boundary problems.