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 ()).
Nous nous intéressons dans cet article aux propriétés dispersives du système des ondes de surface en dimension , 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 ()).
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
@article{ASENS_2011_4_44_5_855_0, author = {Alazard, Thomas and Burq, Nicolas and Zuily, Claude}, title = {Strichartz estimates for water waves}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {855--903}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 44}, number = {5}, year = {2011}, doi = {10.24033/asens.2156}, mrnumber = {2931520}, zbl = {1260.35140}, language = {en}, url = {http://www.numdam.org/articles/10.24033/asens.2156/} }
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 SP - 855 EP - 903 VL - 44 IS - 5 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/asens.2156/ DO - 10.24033/asens.2156 LA - en ID - ASENS_2011_4_44_5_855_0 ER -
%0 Journal Article %A Alazard, Thomas %A Burq, Nicolas %A Zuily, Claude %T Strichartz estimates for water waves %J Annales scientifiques de l'École Normale Supérieure %D 2011 %P 855-903 %V 44 %N 5 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/asens.2156/ %R 10.24033/asens.2156 %G en %F ASENS_2011_4_44_5_855_0
Alazard, Thomas; Burq, Nicolas; Zuily, Claude. Strichartz estimates for water waves. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 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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