Strichartz estimates for water waves

Thomas Alazard; Nicolas Burq; Claude Zuily

Annales scientifiques de l'École Normale Supérieure (2011)

  • Volume: 44, Issue: 5, page 855-903
  • ISSN: 0012-9593

Abstract

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In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system with surface tension. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to construct the solutions in [3]. On the other hand, for smoother initial data, we prove that the solutions enjoy the optimal Strichartz estimates (i.e, without loss of regularity compared to the system linearized at ( η = 0 , ψ = 0 )).

How to cite

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Alazard, Thomas, Burq, Nicolas, and Zuily, Claude. "Strichartz estimates for water waves." Annales scientifiques de l'École Normale Supérieure 44.5 (2011): 855-903. <http://eudml.org/doc/272209>.

@article{Alazard2011,
abstract = {In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system with surface tension. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to construct the solutions in [3]. On the other hand, for smoother initial data, we prove that the solutions enjoy the optimal Strichartz estimates (i.e, without loss of regularity compared to the system linearized at ($\eta =0, \psi = 0$)).},
author = {Alazard, Thomas, Burq, Nicolas, Zuily, Claude},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Euler equation; free boundary problems; water-waves; Cauchy theory; dispersive estimates},
language = {eng},
number = {5},
pages = {855-903},
publisher = {Société mathématique de France},
title = {Strichartz estimates for water waves},
url = {http://eudml.org/doc/272209},
volume = {44},
year = {2011},
}

TY - JOUR
AU - Alazard, Thomas
AU - Burq, Nicolas
AU - Zuily, Claude
TI - Strichartz estimates for water waves
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2011
PB - Société mathématique de France
VL - 44
IS - 5
SP - 855
EP - 903
AB - In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system with surface tension. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to construct the solutions in [3]. On the other hand, for smoother initial data, we prove that the solutions enjoy the optimal Strichartz estimates (i.e, without loss of regularity compared to the system linearized at ($\eta =0, \psi = 0$)).
LA - eng
KW - Euler equation; free boundary problems; water-waves; Cauchy theory; dispersive estimates
UR - http://eudml.org/doc/272209
ER -

References

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