Well-posedness of the free-surface incompressible Euler equations with or without surface tension
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Open Access
- 5 March 2007
- journal article
- Published by American Mathematical Society (AMS) in Journal of the American Mathematical Society
- Vol. 20 (3) , 829-930
- https://doi.org/10.1090/s0894-0347-07-00556-5
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.Keywords
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