[Estimations de Strichartz améliorées par randomisation et EDPs bien-posées avec données initiales surcritiques]
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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Keywords: wave equation, Strichartz estimates, randomised data
Mot clés : équation d’ondes, estimations de Strichartz, données randomisées
@article{AIF_2021__71_5_1929_0,
author = {Burq, Nicolas and Krieger, Joachim},
title = {Randomization improved {Strichartz} estimates and global well-posedness for supercritical data},
journal = {Annales de l'Institut Fourier},
pages = {1929--1961},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {71},
number = {5},
year = {2021},
doi = {10.5802/aif.3448},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3448/}
}
TY - JOUR AU - Burq, Nicolas AU - Krieger, Joachim TI - Randomization improved Strichartz estimates and global well-posedness for supercritical data JO - Annales de l'Institut Fourier PY - 2021 SP - 1929 EP - 1961 VL - 71 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3448/ DO - 10.5802/aif.3448 LA - en ID - AIF_2021__71_5_1929_0 ER -
%0 Journal Article %A Burq, Nicolas %A Krieger, Joachim %T Randomization improved Strichartz estimates and global well-posedness for supercritical data %J Annales de l'Institut Fourier %D 2021 %P 1929-1961 %V 71 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3448/ %R 10.5802/aif.3448 %G en %F AIF_2021__71_5_1929_0
Burq, Nicolas; Krieger, Joachim. Randomization improved Strichartz estimates and global well-posedness for supercritical data. Annales de l'Institut Fourier, Tome 71 (2021) no. 5, pp. 1929-1961. doi : 10.5802/aif.3448. http://www.numdam.org/articles/10.5802/aif.3448/
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