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The Schrödinger equation with spatial white noise potential

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Debussche, Arnaud and Weber, Hendrik (2018) The Schrödinger equation with spatial white noise potential. Electronic Journal of Probability, 23 . pp. 1-16. 28. doi:10.1214/18-EJP143 ISSN 1083-6489.

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Official URL: http://doi.org/10.1214/18-EJP143

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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.

Item Type: Journal Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Schrödinger equation, Renormalization (Physics)
Journal or Publication Title: Electronic Journal of Probability
Publisher: University of Washington. Dept. of Mathematics
ISSN: 1083-6489
Official Date: 30 March 2018
Dates:
DateEvent
30 March 2018Available
16 January 2018Accepted
Volume: 23
Page Range: pp. 1-16
Article Number: 28
DOI: 10.1214/18-EJP143
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 13 March 2018
Date of first compliant Open Access: 8 May 2018
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
DMS-1440140National Science Foundationhttp://dx.doi.org/10.13039/100000001
ANR-11-LABX-0020-01Agence Nationale de la Recherchehttp://dx.doi.org/10.13039/501100001665
UF140187Royal Societyhttp://dx.doi.org/10.13039/501100000288
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