The Schrödinger equation with spatial white noise potential

Arnaud Debussche; Hendrik Weber

doi:10.1214/18-EJP143

The Schrödinger equation with spatial white noise potential

Arnaud Debussche, Hendrik Weber

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

20 Citations (SciVal)

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	https://doi.org/10.1214/18-EJP143
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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10.1214/18-EJP143Licence: CC BY

Cite this

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abstract = "We consider the linear and nonlinear Schr{\"o}dinger 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.",

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KW - Renormalization

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The Schrödinger equation with spatial white noise potential

Abstract

Keywords

ASJC Scopus subject areas

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