We study the asymptotic limit as the density ratio -/+0, where + and - are the densities of two perfect incompressible 2-D/3-D fluids, separated by a surface of discontinuity along which the pressure jump is proportional to the mean curvature of the moving surface. Mathematically, the fluid motion is governed by the two-phase incompressible Euler equations with vortex sheet data. By rescaling, we assume the density + of the inner fluid is fixed, while the density - of the outer fluid is set to epsilon. We prove that solutions of the free-boundary Euler equations in vacuum are obtained in the limit as epsilon 0.
