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Unconditional uniqueness results for the nonlinear Schrödinger equation
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Herr, Sebastian and Sohinger, Vedran (2018) Unconditional uniqueness results for the nonlinear Schrödinger equation. Communications in Contemporary Mathematics . doi:10.1142/S021919971850058X (In Press)
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WRAP-unconditional-uniqueness-results-nonlinear-Schrödinger-equation-Sohinger-2018.pdf - Accepted Version - Requires a PDF viewer. Download (857Kb) | Preview |
Official URL: https://doi.org/10.1142/S021919971850058X
Abstract
We study the problem of unconditional uniqueness of solutions to the cubic nonlinear Schrödinger equation (NLS). We introduce a new strategy to approach this problem on bounded domains, in particular on rectangular tori. It is a known fact that solutions to the cubic NLS give rise to solutions of the Gross–Pitaevskii (GP) hierarchy, which is an infinite-dimensional system of linear equations. By using the uniqueness analysis of the GP hierarchy, we obtain new unconditional uniqueness results for the cubic NLS on rectangular tori, which cover the full scaling-subcritical regime in high dimensions. In fact, we prove a more general result which is conditional on the domain. In addition, we observe that well-posedness of the cubic NLS in Fourier–Lebesgue spaces implies unconditional uniqueness.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QC Physics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Schrödinger equation, Gross-Pitaevskii equations | ||||||
| Journal or Publication Title: | Communications in Contemporary Mathematics | ||||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||
| ISSN: | 0219-1997 | ||||||
| Official Date: | 30 August 2018 | ||||||
| Dates: |
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| Date of first compliant deposit: | 15 August 2018 | ||||||
| DOI: | 10.1142/S021919971850058X | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | In Press | ||||||
| Publisher Statement: | Electronic version of an article published as [Journal, Volume, Issue, Year, Pages] 10.1142/S021919971850058X © 2018 copyright World Scientific Publishing company https://www.worldscientific.com/worldscinet/ccm | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| RIOXX Funder/Project Grant: |
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