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.

Reçu le :
Accepté le :
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DOI : 10.5802/jep.168
Classification : 35R01, 35A17, 35B45, 35L10, 35L20
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

1 Sorbonne Université, CNRS, Laboratoire Jacques-Louis Lions, LJLL F-75005 Paris, France
2 Université Côte d’Azur, CNRS, Laboratoire JAD 06108 Nice Cedex 02, France
3 Sorbonne Université, CNRS, Institut Mathématique de Jussieu-Paris Rive Gauche, IMJ-PRG F-75005 Paris, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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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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