Scattering for stochastic nonlinear Schrödinger equations

Herr S, Röckner M, Zhang D (2019)
Communications in Mathematical Physics 368(2): 843–884.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We study the scattering behavior of global solutions to stochastic nonlinear Schr\"odinger equations with linear multiplicative noise. In the case where the quadratic variation of the noise is globally finite and the nonlinearity is defocusing,we prove that the solutions scatter at infinity in the pseudo-conformal space and in the energy space respectively, including the energy-critical case. Moreover, in the case where the noise is large, non-conservative and has infinite quadratic variation, we show that the solutions scatter at infinity with high probability for all energy-subcritical exponents.
Erscheinungsjahr
2019
Zeitschriftentitel
Communications in Mathematical Physics
Band
368
Ausgabe
2
Seite(n)
843–884
eISSN
1432-0916
Page URI
https://pub.uni-bielefeld.de/record/2934350

Zitieren

Herr S, Röckner M, Zhang D. Scattering for stochastic nonlinear Schrödinger equations. Communications in Mathematical Physics. 2019;368(2):843–884.
Herr, S., Röckner, M., & Zhang, D. (2019). Scattering for stochastic nonlinear Schrödinger equations. Communications in Mathematical Physics, 368(2), 843–884. doi:10.1007/s00220-019-03429-0
Herr, S., Röckner, M., and Zhang, D. (2019). Scattering for stochastic nonlinear Schrödinger equations. Communications in Mathematical Physics 368, 843–884.
Herr, S., Röckner, M., & Zhang, D., 2019. Scattering for stochastic nonlinear Schrödinger equations. Communications in Mathematical Physics, 368(2), p 843–884.
S. Herr, M. Röckner, and D. Zhang, “Scattering for stochastic nonlinear Schrödinger equations”, Communications in Mathematical Physics, vol. 368, 2019, pp. 843–884.
Herr, S., Röckner, M., Zhang, D.: Scattering for stochastic nonlinear Schrödinger equations. Communications in Mathematical Physics. 368, 843–884 (2019).
Herr, Sebastian, Röckner, Michael, and Zhang, Deng. “Scattering for stochastic nonlinear Schrödinger equations”. Communications in Mathematical Physics 368.2 (2019): 843–884.
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arXiv: 1804.10429

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