# 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

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topAlazard, 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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