The Schrödinger equation with spatial white noise potential

Arnaud Debussche (1, 2, 3) , Hendrik Weber (4)

1 MINGUS - Multi-scale numerical geometric schemes
2 ENS Rennes - École normale supérieure - Rennes
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 WMI - Warwick Mathematics Institute

We consider the linear and nonlinear Schrödinger equation with a spatial white noise as a potential over the two dimensional torus. We prove existence and uniqueness of solutions to an initial value problem for suitable initial data. Our construction is based on a change of unknown originally used in [13] and conserved quantities.

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

Arnaud Debussche, Hendrik Weber. The Schrödinger equation with spatial white noise potential. Electronic Journal of Probability, 2018, 23, pp.1-16. ⟨hal-01942694⟩