New counterexamples to Strichartz estimates for the wave equation on a 2D model convex domain
[Nouveaux contre-exemples aux estimations de Strichartz pour l’équation des ondes dans un domaine convexe modèle bidimensionnel]
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021) , pp. 1133-1157.

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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Accepté le :
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DOI : https://doi.org/10.5802/jep.168
Classification : 35R01,  35A17,  35B45,  35L10,  35L20
Mots clés : Équation des ondes, estimations de Strichartz, domaines à bord
@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/}
}
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, Tome 8 (2021) , pp. 1133-1157. doi : 10.5802/jep.168. https://jep.centre-mersenne.org/articles/10.5802/jep.168/

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