[Mesures de Gibbs et équations non-linéaires des ondes et de Schrödinger sur la boule]
On démontre des résultats nouveaux sur les solutions radiales de lʼéquation des ondes et lʼéquation de Schrödinger sur la boule B dans et pour des conditions initiales aléatoires. Plus exactement, on établit une dynamique bien définie et unique sur le support de la mesure de Gibbs. Ceci complète des résultats de Burq et Tzvetkov (2008) [8,9] et Tzvetkov (2006, 2008) [10,11].
We establish new results for the radial nonlinear wave and Schrödinger equations on the ball in and , for random initial data. More precisely, a well-defined and unique dynamics is obtained on the support of the corresponding Gibbs measure. This complements results from Burq and Tzvetkov (2008) [8,9] and Tzvetkov (2006, 2008) [10,11].
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@article{CRMATH_2012__350_11-12_571_0,
author = {Bourgain, Jean and Bulut, Aynur},
title = {Gibbs measure evolution in radial nonlinear wave and {Schr\"odinger} equations on the ball},
journal = {Comptes Rendus. Math\'ematique},
pages = {571--575},
publisher = {Elsevier},
volume = {350},
number = {11-12},
year = {2012},
doi = {10.1016/j.crma.2012.05.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.05.006/}
}
TY - JOUR AU - Bourgain, Jean AU - Bulut, Aynur TI - Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball JO - Comptes Rendus. Mathématique PY - 2012 SP - 571 EP - 575 VL - 350 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.05.006/ DO - 10.1016/j.crma.2012.05.006 LA - en ID - CRMATH_2012__350_11-12_571_0 ER -
%0 Journal Article %A Bourgain, Jean %A Bulut, Aynur %T Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball %J Comptes Rendus. Mathématique %D 2012 %P 571-575 %V 350 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.05.006/ %R 10.1016/j.crma.2012.05.006 %G en %F CRMATH_2012__350_11-12_571_0
Bourgain, Jean; Bulut, Aynur. Gibbs measure evolution in radial nonlinear wave and Schrödinger equations on the ball. Comptes Rendus. Mathématique, Tome 350 (2012) no. 11-12, pp. 571-575. doi : 10.1016/j.crma.2012.05.006. http://www.numdam.org/articles/10.1016/j.crma.2012.05.006/
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☆ The research of J.B. was partially supported by NSF grants DMS-0808042 and DMS-0835373 and the research of A.B. was supported by NSF under agreement Nos. DMS-0635607 and DMS-0808042.
