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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Well-posedness of the free-surface incompressible Euler equations with or without surface tension
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by Daniel Coutand and Steve Shkoller PDF
J. Amer. Math. Soc. 20 (2007), 829-930 Request permission

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
  • 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