Journal of the American Mathematical Society

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
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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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Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 35Q35, 35R35, 35Q05, 76B03

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
Email: shkoller@math.ucdavis.edu

DOI: 10.1090/S0894-0347-07-00556-5
PII: S 0894-0347(07)00556-5
Keywords: Euler equations, free boundary problems, surface tension
Received by editor(s): November 9, 2005
Posted: March 5, 2007
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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

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