Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation

Herr S, Sohinger V (2019)
Communications in Contemporary Mathematics 21(7): 1850058.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor/in
Herr, SebastianUniBi ; Sohinger, Vedran
Abstract / Bemerkung
We study the problem of unconditional uniqueness of solutions to the cubic nonlinear Schr\"odinger 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.
Erscheinungsjahr
2019
Zeitschriftentitel
Communications in Contemporary Mathematics
Band
21
Ausgabe
7
Art.-Nr.
1850058
ISSN
0219-1997
eISSN
1793-6683
Page URI
https://pub.uni-bielefeld.de/record/2934335

Zitieren

Herr S, Sohinger V. Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation. Communications in Contemporary Mathematics. 2019;21(7): 1850058.
Herr, S., & Sohinger, V. (2019). Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation. Communications in Contemporary Mathematics, 21(7), 1850058. doi:10.1142/S021919971850058X
Herr, S., and Sohinger, V. (2019). Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation. Communications in Contemporary Mathematics 21:1850058.
Herr, S., & Sohinger, V., 2019. Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation. Communications in Contemporary Mathematics, 21(7): 1850058.
S. Herr and V. Sohinger, “Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation”, Communications in Contemporary Mathematics, vol. 21, 2019, : 1850058.
Herr, S., Sohinger, V.: Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation. Communications in Contemporary Mathematics. 21, : 1850058 (2019).
Herr, Sebastian, and Sohinger, Vedran. “Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation”. Communications in Contemporary Mathematics 21.7 (2019): 1850058.

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