Global dissipative martingale solutions to the variational wave equation with stochastic forcing

Billel Guelmame (1, 2) , Julien Vovelle (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 Université de Lyon

We consider the variational wave equation in one-dimensional space with stochastic forcing by an additive noise. Blow-up of local smooth solutions is established, and global existence is proved in the class of weak martingale solutions.

Mots clés: Stochastic PDEs; Hyperbolic equations; Wave equation; Blow-up; Young measure; Skorokhod--Jakubowski's representation theorem

Domaines: Mathématiques [math]

Billel Guelmame, Julien Vovelle. Global dissipative martingale solutions to the variational wave equation with stochastic forcing. 2023. ⟨hal-04282928⟩