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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 in Sobolev spaces of the full water wave problem in 3-D
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by Sijue Wu PDF
J. Amer. Math. Soc. 12 (1999), 445-495 Request permission

Abstract:

We consider the motion of the interface of a 3-D inviscid, incompressible, irrotational water wave, with air region above water region and surface tension zero. We prove that the motion of the interface of the water wave is not subject to Taylor instability, as long as the interface separates the whole 3-D space into two simply connected $C^{2}$ regions. We prove further the existence and uniqueness of solutions of the full 3-D water wave problem, locally in time, for any initial interface that separates the whole 3-D space into two simply connected regions.
References
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Additional Information
  • Sijue Wu
  • Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
  • Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742
  • Email: swu@math.uiowa.edu, sijue@math.umd.edu
  • Received by editor(s): December 15, 1997
  • Received by editor(s) in revised form: August 24, 1998
  • Additional Notes: 1991 Financial support provided in part by NSF grant DMS-9600141 and the J. Seward Johnson Sr. Charitable Trust.
  • © Copyright 1999 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 12 (1999), 445-495
  • MSC (1991): Primary 76B15; Secondary 35L99, 35R35
  • DOI: https://doi.org/10.1090/S0894-0347-99-00290-8
  • MathSciNet review: 1641609