[Nouveaux contre-exemples aux estimations de Strichartz pour l’équation des ondes dans un domaine convexe modèle bidimensionnel]
Nous démontrons que le domaine de validité des estimations de Strichartz sur un domaine convexe modèle bidimensionnel peut être encore restreint par rapport aux contre-exemples déjà connus [3, 4]. Notre nouvelle famille de contre-exemples s’appuie sur la construction de parametrix élaborée dans [7] et revisitée dans [8]. Cette construction est en sus optimale dans certaines régions de l’espace des phases.
We prove that the range of Strichartz estimates on a model 2D convex domain may be further restricted compared to the known counterexamples from [3, 4]. Our new family of counterexamples is built on the parametrix construction from [7] and revisited in [8]. Interestingly enough, it is sharp in at least some regions of phase space.
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Keywords: Dispersive estimates, wave equation, Dirichlet boundary condition
Mot clés : Équation des ondes, estimations de Strichartz, domaines à bord
@article{JEP_2021__8__1133_0,
author = {Ivanovici, Oana and Lebeau, Gilles and Planchon, Fabrice},
title = {New counterexamples to {Strichartz} estimates for the wave equation on a $2${D} model convex domain},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1133--1157},
publisher = {Ecole polytechnique},
volume = {8},
year = {2021},
doi = {10.5802/jep.168},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jep.168/}
}
TY - JOUR AU - Ivanovici, Oana AU - Lebeau, Gilles AU - Planchon, Fabrice TI - New counterexamples to Strichartz estimates for the wave equation on a $2$D model convex domain JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 1133 EP - 1157 VL - 8 PB - Ecole polytechnique UR - http://www.numdam.org/articles/10.5802/jep.168/ DO - 10.5802/jep.168 LA - en ID - JEP_2021__8__1133_0 ER -
%0 Journal Article %A Ivanovici, Oana %A Lebeau, Gilles %A Planchon, Fabrice %T New counterexamples to Strichartz estimates for the wave equation on a $2$D model convex domain %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 1133-1157 %V 8 %I Ecole polytechnique %U http://www.numdam.org/articles/10.5802/jep.168/ %R 10.5802/jep.168 %G en %F JEP_2021__8__1133_0
Ivanovici, Oana; Lebeau, Gilles; Planchon, Fabrice. New counterexamples to Strichartz estimates for the wave equation on a $2$D model convex domain. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1133-1157. doi : 10.5802/jep.168. http://www.numdam.org/articles/10.5802/jep.168/
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