New counterexamples to Strichartz estimates for the wave equation on a 2D model convex domain
Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 1133-1157.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.168
Classification: 35R01,  35A17,  35B45,  35L10,  35L20
Keywords: Dispersive estimates, wave equation, Dirichlet boundary condition
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
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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, 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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