## 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.## References

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## Bibliographic Information

**Daniel Coutand**- Affiliation: Department of Mathematics, University of California at Davis, Davis, California 95616
- Email: coutand@math.ucdavis.edu
**Steve Shkoller**- Affiliation: Department of Mathematics, University of California at Davis, Davis, California 95616
- MR Author ID: 353659
- Email: shkoller@math.ucdavis.edu
- Received by editor(s): November 9, 2005
- Published electronically: March 5, 2007
- © Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**20**(2007), 829-930 - MSC (2000): Primary 35Q35, 35R35, 35Q05, 76B03
- DOI: https://doi.org/10.1090/S0894-0347-07-00556-5
- MathSciNet review: 2291920