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arXiv:math/0511236 [math.AP]AbstractReferencesReviewsResources

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

Daniel Coutand, Steve Shkoller

Published 2005-11-09, updated 2006-11-15Version 3

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.

Comments: To appear in J. Amer. Math. Soc., 96 pages
Categories: math.AP, math-ph, math.MP
Subjects: 35Q35, 35R35, 35Q05, 76B03
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