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

Jean-Claude Saut; Nikolay Tzvetkov

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 2, page 501-523
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Saut, Jean-Claude, and Tzvetkov, Nikolay. "On a model system for the oblique interaction of internal gravity waves." ESAIM: Mathematical Modelling and Numerical Analysis 34.2 (2010): 501-523. <http://eudml.org/doc/197558>.

@article{Saut2010,
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. },
author = {Saut, Jean-Claude, Tzvetkov, Nikolay},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Internal gravity waves; Kadomtsev-Petviashvili equations; Cauchy problem.; oblique interaction of nonlinear internal waves; global well-posedness; smoothing effect; Fourier transform; Strichartz estimates; lower-order perturbation},
language = {eng},
month = {3},
number = {2},
pages = {501-523},
publisher = {EDP Sciences},
title = {On a model system for the oblique interaction of internal gravity waves},
url = {http://eudml.org/doc/197558},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Saut, Jean-Claude
AU - Tzvetkov, Nikolay
TI - On a model system for the oblique interaction of internal gravity waves
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 2
SP - 501
EP - 523
AB - 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.
LA - eng
KW - Internal gravity waves; Kadomtsev-Petviashvili equations; Cauchy problem.; oblique interaction of nonlinear internal waves; global well-posedness; smoothing effect; Fourier transform; Strichartz estimates; lower-order perturbation
UR - http://eudml.org/doc/197558
ER -

References

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