[Solutions globales d'énergie infinie pour l'équation des ondes cubique]
We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.
On considère l'équation des ondes cubique sur un tore de dimension supérieure à 3, et on montre l'existence de solutions globales d'énergie infinie. La condition initiale de l'équation est un élément typique du support d'une mesure de probabilité.
DOI : 10.24033/bsmf.2688
Keywords: Nonlinear wave equation, random data, weak solutions, global solutions
Mots-clés : Équation des ondes non-linéaire, conditions initiales aléatoires, solutions faibles, solutions globales.
@article{BSMF_2015__143_2_301_0,
author = {Burq, Nicolas and Thomann, Laurent and Tzvetkov, Nikolay},
title = {Global infinite energy solutions for the cubic wave equation},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {301--313},
year = {2015},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {143},
number = {2},
doi = {10.24033/bsmf.2688},
mrnumber = {3351181},
zbl = {1320.35217},
language = {en},
url = {https://www.numdam.org/articles/10.24033/bsmf.2688/}
}
TY - JOUR AU - Burq, Nicolas AU - Thomann, Laurent AU - Tzvetkov, Nikolay TI - Global infinite energy solutions for the cubic wave equation JO - Bulletin de la Société Mathématique de France PY - 2015 SP - 301 EP - 313 VL - 143 IS - 2 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2688/ DO - 10.24033/bsmf.2688 LA - en ID - BSMF_2015__143_2_301_0 ER -
%0 Journal Article %A Burq, Nicolas %A Thomann, Laurent %A Tzvetkov, Nikolay %T Global infinite energy solutions for the cubic wave equation %J Bulletin de la Société Mathématique de France %D 2015 %P 301-313 %V 143 %N 2 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2688/ %R 10.24033/bsmf.2688 %G en %F BSMF_2015__143_2_301_0
Burq, Nicolas; Thomann, Laurent; Tzvetkov, Nikolay. Global infinite energy solutions for the cubic wave equation. Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 2, pp. 301-313. doi: 10.24033/bsmf.2688
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