2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104857We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface 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.To appear in J. Amer. Math. Soc., 96 pagesAnalysis of PDEsMathematical Physics35Q35, 35R35, 35Q05, 76B03text