1D quintic nonlinear Schrödinger equation with white noise dispersion

Arnaud Debussche (1, 2) , Yoshio Tsutsumi (3)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Department of Mathematics [Kyoto]

In this article, we improve the Strichartz estimates obtained in [12] for the Schrödinger equation with white noise dispersion in one dimension. This allows us to prove global well posedness when a quintic critical nonlinearity is added to the equation. We finally show that the white noise dispersion is the limit of smooth random dispersion.

Mots clés: nonlinear Schrödinger; white noise dispersion; Strichartz estimates; stochastic partial differential equation

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

Arnaud Debussche, Yoshio Tsutsumi. 1D quintic nonlinear Schrödinger equation with white noise dispersion. Journal de Mathématiques Pures et Appliquées, 2011, 96 (4), pp.363-376. ⟨10.1016/j.matpur.2011.02.002⟩. ⟨hal-00527508⟩