Well-posedness of the Free-surface Incompressible Euler Equations with or without Surface Tension

Abstract

We develop a new methodology for treating free boundary problems in mechanics, and use it to prove local-in-time well-posedness in Sobolev spaces for the freesurface 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.

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@inproceedings{Coutand2005WellposednessOT, title={Well-posedness of the Free-surface Incompressible Euler Equations with or without Surface Tension}, author={Daniel Coutand and Steve Shkoller}, year={2005} }