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On a model system for the oblique interaction of internal gravity waves

Published online by Cambridge University Press:  15 April 2002

Jean-Claude Saut  and
Nikolay Tzvetkov
Jean-Claude Saut
Affiliation:
Analyse numérique et EDP, Université de Paris-Sud, Bt. 425, 91405 Orsay Cedex, France. (Jean-Claude.saut@math.u-psud.fr)
Nikolay Tzvetkov
Affiliation:
Analyse numérique et EDP, Université de Paris-Sud, Bât. 425, 91405 Orsay Cedex, France. (Nikolay.tzvetkov@math.u-psud.fr )
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Abstract

We give local and global well-posedness results for a system of two Kadomtsev-Petviashvili (KP) equations derived by R. Grimshaw and Y. Zhu to model the oblique interaction of weakly nonlinear, two dimensional, long internal waves in shallow fluids. We also prove a smoothing effect for the amplitudes of the interacting waves. We use the Fourier transform restriction norms introduced by J. Bourgain and the Strichartz estimates for the linear KP group. Finally we extend the result of [3] for lower order perturbation of the system in the absence of transverse effects.

Keywords

Internal gravity wavesKadomtsev-Petviashvili equationsCauchy problem.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 2: Special issue for R. Teman's 60th birthday , March 2000 , pp. 501 - 523
Copyright
© EDP Sciences, SMAI, 2000

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