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Well-posedness in Sobolev spaces of the full water wave problem in 3-D
Author(s):
Sijue
Wu
Journal:
J. Amer. Math. Soc.
12
(1999),
445-495.
MSC (1991):
Primary 76B15;
Secondary 35L99, 35R35
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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  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
Email:
swu@math.uiowa.edu, sijue@math.umd.edu
DOI:
10.1090/S0894-0347-99-00290-8
PII:
S 0894-0347(99)00290-8
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 of article:
Copyright
1999,
American Mathematical Society
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