Abstract
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.
| Original language | English |
|---|---|
| Article number | 28 |
| Number of pages | 16 |
| Journal | Electronic Journal of Probability |
| Volume | 23 |
| Early online date | 30 Mar 2018 |
| DOIs | |
| Publication status | Published - 2018 |
Keywords
- Nonlinear Schrödinger equation
- Renormalization
- Spatial white noise
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
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