Randomization improved Strichartz estimates and global well-posedness for supercritical data
Annales de l'Institut Fourier, Volume 71 (2021) no. 5, pp. 1929-1961.

We introduce a novel data randomisation for the free wave equation which leads to the same range of Strichartz estimates as for radial data, albeit in a non-radial context. We then use these estimates to establish global well-posedness for a wave maps type nonlinear wave equation for certain supercritical data, provided the data are suitably small and randomised.

On introduit une nouvelle randomisation des données initiales pour l’équation des ondes, telle que les solutions satisfont les mêmes estimations de Strichartz que dans le cadre radial, au dépit de leur caractère non-radial. Nous utilisons ces estimations pour montrer que certaines équations modèles similaires aux applications d’ondes sont bien-posées pour des données initiales surcritiques.

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DOI: 10.5802/aif.3448
Classification: 35L05, 35B40
Keywords: wave equation, Strichartz estimates, randomised data
Mot clés : équation d’ondes, estimations de Strichartz, données randomisées

Burq, Nicolas 1; Krieger, Joachim 2

1 Laboratoire de Mathématiques d’Orsay Université Paris-Saclay Bat. 307, 91405 Orsay Cedex (France) and Institut Universitaire de France
2 Bâtiment des Mathématiques, EPFL Station 8, CH-1015 Lausanne, CH-1015 Lausanne (Switzerland)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Randomization improved {Strichartz} estimates and global well-posedness for supercritical data},
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Burq, Nicolas; Krieger, Joachim. Randomization improved Strichartz estimates and global well-posedness for supercritical data. Annales de l'Institut Fourier, Volume 71 (2021) no. 5, pp. 1929-1961. doi : 10.5802/aif.3448. https://aif.centre-mersenne.org/articles/10.5802/aif.3448/

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