Global infinite energy solutions for the cubic wave equation

Nicolas Burq (1) , Laurent Thomann (2) , Nikolay Tzvetkov (3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

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.

Mots clés: global solutions; Nonlinear wave equation; random data; weak solutions; global solutions.

Domaines: Equations aux dérivées partielles [math.AP]; Mathématiques [math]

Nicolas Burq, Laurent Thomann, Nikolay Tzvetkov. Global infinite energy solutions for the cubic wave equation. Bulletin de la société mathématique de France, 2015, 143 (2), pp.301--313. ⟨hal-00739276⟩