no. 5
Strichartz estimates for water waves
[Estimées de Strichartz pour les ondes de surface]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 44 (2011) no. 5, pp. 855-903.

Nous nous intéressons dans cet article aux propriétés dispersives du système des ondes de surface en dimension 2, avec tension de surface. Nous démontrons tout d’abord des estimées de Strichartz, avec pertes de dérivées, au niveau de régularité où nous avons construit des solutions dans [3]. Ensuite, pour des données initiales plus régulières, nous démontrons les estimées de Strichartz optimales (i.e. sans perte de régularité par rapport à celles du système linéarisé en (η=0,ψ=0)).

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)).

DOI : 10.24033/asens.2156
Classification : 35Bxx, 35Lxx, 35Sxx, 35Jxx
Keywords: Euler equation, free boundary problems, water-waves, Cauchy theory, dispersive estimates
Mot clés : Équation d'Euler, problèmes à frontière libre, ondes de surfaces, théorie de Cauchy, estimées dispersives 
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     title = {Strichartz estimates for water waves},
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Alazard, Thomas; Burq, Nicolas; Zuily, Claude. Strichartz estimates for water waves. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 44 (2011) no. 5, pp. 855-903. doi : 10.24033/asens.2156. http://www.numdam.org/articles/10.24033/asens.2156/

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