Randomization improved Strichartz estimates and global well-posedness for supercritical data
[Estimations de Strichartz améliorées par randomisation et EDPs bien-posées avec données initiales surcritiques]
Annales de l'Institut Fourier, Online first, 33 p.

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.

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.

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DOI : https://doi.org/10.5802/aif.3448
Classification : 35L05,  35B40
Mots clés : équation d’ondes, estimations de Strichartz, données randomisées
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Burq, Nicolas; Krieger, Joachim. Randomization improved Strichartz estimates and global well-posedness for supercritical data. Annales de l'Institut Fourier, Online first, 33 p.

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