The Schrödinger equation with spatial white noise potential

Arnaud Debussche, Hendrik Weber

Research output: Contribution to journalArticlepeer-review

11 Citations (SciVal)


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 languageEnglish
Article number28
Number of pages16
JournalElectronic Journal of Probability
Early online date30 Mar 2018
Publication statusPublished - 2018


  • Nonlinear Schrödinger equation
  • Renormalization
  • Spatial white noise

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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