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ISSN 1088-6834(e) ISSN 0894-0347(p)

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

Author(s): Daniel Coutand; Steve Shkoller
Journal: J. Amer. Math. Soc. 20 (2007), 829-930.
MSC (2000): Primary 35Q35, 35R35, 35Q05, 76B03
Posted: March 5, 2007
MathSciNet review: 2291920
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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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