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

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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 > 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:	Date Event 30 March 2018 Available 16 January 2018 Accepted
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
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID DMS-1440140 National Science Foundation http://dx.doi.org/10.13039/100000001 ANR-11-LABX-0020-01 Agence Nationale de la Recherche http://dx.doi.org/10.13039/501100001665 UF140187 Royal Society http://dx.doi.org/10.13039/501100000288
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