Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Analysis of PDEs

arXiv:1804.10631 (math)
[Submitted on 27 Apr 2018 (v1), last revised 22 Oct 2018 (this version, v2)]

Title:Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation

Authors:Sebastian Herr, Vedran Sohinger
View PDF
Abstract:We study the problem of unconditional uniqueness of solutions to the cubic nonlinear Schrödinger equation. 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 hierarchy, which is an infinite-dimensional system of linear equations. By using the uniqueness analysis of the Gross-Pitaevskii 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.
Comments: version 2: minor corrections
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35Q55
Cite as: arXiv:1804.10631 [math.AP]
  (or arXiv:1804.10631v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.10631
Journal reference: Commun. Contemp. Math. (2019), Vol. 21, No. 7, 1850058, 33 pp
Related DOI: https://doi.org/10.1142/S021919971850058X

Submission history

From: Sebastian Herr [view email]
[v1] Fri, 27 Apr 2018 18:05:02 UTC (29 KB)
[v2] Mon, 22 Oct 2018 11:46:53 UTC (29 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.AP
< prev   |   next >
new | recent | 2018-04
Change to browse by:
math

References & Citations

1 blog link

(what is this?)
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)