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Well-posedness in Sobolev spaces
of the full water wave problem in 3-D

Author: Sijue Wu
Journal: J. Amer. Math. Soc. 12 (1999), 445-495
MSC (1991): Primary 76B15; Secondary 35L99, 35R35
MathSciNet review: 1641609
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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.

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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

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.
Article copyright: © Copyright 1999 American Mathematical Society

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