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.
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.
Accepted:
Published online:
Keywords: Dispersive estimates, wave equation, Dirichlet boundary condition
Mot clés : Équation des ondes, estimations de Strichartz, domaines à bord
Oana Ivanovici 1; Gilles Lebeau 2; Fabrice Planchon 3
CC-BY 4.0
@article{JEP_2021__8__1133_0,
author = {Oana Ivanovici and Gilles Lebeau and Fabrice Planchon},
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 = {https://jep.centre-mersenne.org/articles/10.5802/jep.168/}
}
TY - JOUR AU - Oana Ivanovici AU - Gilles Lebeau AU - Fabrice Planchon 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 - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.168/ DO - 10.5802/jep.168 LA - en ID - JEP_2021__8__1133_0 ER -
%0 Journal Article %A Oana Ivanovici %A Gilles Lebeau %A Fabrice Planchon %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 École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.168/ %R 10.5802/jep.168 %G en %F JEP_2021__8__1133_0
Oana Ivanovici; Gilles Lebeau; Fabrice Planchon. New counterexamples to Strichartz estimates for the wave equation on a $2$D model convex domain. Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 1133-1157. doi : 10.5802/jep.168. https://jep.centre-mersenne.org/articles/10.5802/jep.168/
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