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

Coutand, Daniel; Shkoller, Steve

doi:10.1090/S0894-0347-07-00556-5

Well-posedness of the free-surface incompressible Euler equations with or without surface tension
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by Daniel Coutand and Steve Shkoller

J. Amer. Math. Soc. 20 (2007), 829-930

DOI: https://doi.org/10.1090/S0894-0347-07-00556-5

Published electronically: March 5, 2007

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Abstract:

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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