Coutand, Daniel; Shkoller, Steve A simple proof of well-posedness for the free-surface incompressible Euler equations. (English) Zbl 1210.35163 Discrete Contin. Dyn. Syst., Ser. S 3, No. 3, 429-449 (2010). Summary: The purpose of this this paper is to present a new simple proof for the construction of unique solutions to the moving free-boundary incompressible 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 applied to a number of other moving free-boundary problems. Cited in 1 ReviewCited in 45 Documents MSC: 35L65 Hyperbolic conservation laws 35L70 Second-order nonlinear hyperbolic equations 35L80 Degenerate hyperbolic equations 35Q35 PDEs in connection with fluid mechanics 35R35 Free boundary problems for PDEs 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids Keywords:Euler; water-waves; free boundary problems; vacuum PDFBibTeX XMLCite \textit{D. Coutand} and \textit{S. Shkoller}, Discrete Contin. Dyn. Syst., Ser. S 3, No. 3, 429--449 (2010; Zbl 1210.35163) Full Text: DOI