Well-posedness of the free-surface incompressible Euler equations with or without surface tension

Details Well-posedness of the free-surface incompressible Euler equations with or without surface tension Well-posedness of the free-surface incompressible Euler equations with or without surface tension

2005-11-09

arxiv.org/abs/math/0511236v3

Mathematics

Analysis of PDEs

To appear in J. Amer. Math. Soc., 96 pages

Scientific paper

We 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.

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