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  and conserved quantities.
- Nonlinear Schrödinger equation
- Spatial white noise
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty