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Communications in Mathematical Physics

, Volume 368, Issue 2, pp 843–884 | Cite as

Scattering for Stochastic Nonlinear Schrödinger Equations

  • Sebastian Herr
  • Michael Röckner
  • Deng ZhangEmail author
Article
  • 176 Downloads

Abstract

We study the scattering behavior of global solutions to stochastic nonlinear Schrödinger 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.

Notes

Acknowledgements

D. Zhang is supported by NSFC (No. 11501362). Financial support by the DFG through CRC 1283 is gratefully acknowledged.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiChina

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