Stochastic nonlinear Schrödinger equations: No blow-up in the non-conservative case

Barbu V, Röckner M, Zhang D (2017)
Journal of Differential Equations 263(11): 7919-7940.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Barbu, Viorel; Röckner, MichaelUniBi; Zhang, Deng
Abstract / Bemerkung
This paper is devoted to the study of noise effects on blow-up solutions to stochastic nonlinear Schrodinger equations. It is a continuation of our recent work [2], where the (local) well-posedness is established in H-1, also in the non-conservative critical case. Here we prove that in the non-conservative focusing mass-(super)critical case, by adding a large multiplicative Gaussian noise, with high probability one can prevent the blow-up on any given bounded time interval [0, T], 0 < T < infinity. Moreover, in the case of spatially independent noise, the explosion even can be prevented with high probability on the whole time interval [0, infinity). The noise effects obtained here are completely different from those in the conservative case studied in [5]. (C) 2017 Elsevier Inc. All rights reserved.
Stichworte
(Stochastic) nonlinear Schrodinger equation; Wiener process; Noise; effect; Blow-up
Erscheinungsjahr
2017
Zeitschriftentitel
Journal of Differential Equations
Band
263
Ausgabe
11
Seite(n)
7919-7940
ISSN
0022-0396
eISSN
1090-2732
Page URI
https://pub.uni-bielefeld.de/record/2914999

Zitieren

Barbu V, Röckner M, Zhang D. Stochastic nonlinear Schrödinger equations: No blow-up in the non-conservative case. Journal of Differential Equations. 2017;263(11):7919-7940.
Barbu, V., Röckner, M., & Zhang, D. (2017). Stochastic nonlinear Schrödinger equations: No blow-up in the non-conservative case. Journal of Differential Equations, 263(11), 7919-7940. doi:10.1016/j.jde.2017.08.030
Barbu, V., Röckner, M., and Zhang, D. (2017). Stochastic nonlinear Schrödinger equations: No blow-up in the non-conservative case. Journal of Differential Equations 263, 7919-7940.
Barbu, V., Röckner, M., & Zhang, D., 2017. Stochastic nonlinear Schrödinger equations: No blow-up in the non-conservative case. Journal of Differential Equations, 263(11), p 7919-7940.
V. Barbu, M. Röckner, and D. Zhang, “Stochastic nonlinear Schrödinger equations: No blow-up in the non-conservative case”, Journal of Differential Equations, vol. 263, 2017, pp. 7919-7940.
Barbu, V., Röckner, M., Zhang, D.: Stochastic nonlinear Schrödinger equations: No blow-up in the non-conservative case. Journal of Differential Equations. 263, 7919-7940 (2017).
Barbu, Viorel, Röckner, Michael, and Zhang, Deng. “Stochastic nonlinear Schrödinger equations: No blow-up in the non-conservative case”. Journal of Differential Equations 263.11 (2017): 7919-7940.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar