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15 June 2011 On the water-wave equations with surface tension
T. Alazard, N. Burq, C. Zuily
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Duke Math. J. 158(3): 413-499 (15 June 2011). DOI: 10.1215/00127094-1345653

Abstract

The purpose of this article is to clarify the Cauchy theory of the water-wave equations in terms of regularity indexes for the initial conditions, as well as for the smoothness of the bottom of the domain. (Namely, no regularity assumption is assumed on the bottom.) Our main result is that, after suitable paralinearization, the system can be arranged into an explicit symmetric system of Schrödinger type. We then show that the smoothing effect for the (one-dimensional) surface-tension water waves is in fact a rather direct consequence of this reduction, and following this approach, we are able to obtain a sharp result in terms of regularity of the indexes of the initial data and weights in the estimates.

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T. Alazard. N. Burq. C. Zuily. "On the water-wave equations with surface tension." Duke Math. J. 158 (3) 413 - 499, 15 June 2011. https://doi.org/10.1215/00127094-1345653

Information

Published: 15 June 2011
First available in Project Euclid: 1 June 2011

zbMATH: 1258.35043
MathSciNet: MR2805065
Digital Object Identifier: 10.1215/00127094-1345653

Subjects:
Primary: 35Bxx
Secondary: 35JXX , 35LXX , 35Sxx

Rights: Copyright © 2011 Duke University Press

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Vol.158 • No. 3 • 15 June 2011
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