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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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


Authors: Daniel Coutand and Steve Shkoller
Journal: J. Amer. Math. Soc. 20 (2007), 829-930
MSC (2000): Primary 35Q35, 35R35, 35Q05, 76B03
Published electronically: 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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Additional 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
Email: shkoller@math.ucdavis.edu

DOI: http://dx.doi.org/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
Published electronically: March 5, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.