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Recent Progress on Stochastic Nonlinear Schrödinger Equations

  • Deng ZhangEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)

Abstract

This note presents the recent results for stochastic nonlinear Schrödinger equations with linear multiplicative noise, including the global well-posedness, the noise effect on blow-up and the optimal bilinear control problem. An important role in the proof is played by the rescaling approach.

Keywords

(Stochastic) Nonlinear Schrödinger equation Maximal monotonicity Noise effect Optimal bilinear control Strichartz estimates 

2010 Mathematics Subject Classification

60H15 60H30 35Q55 47H05 81Q93 

Notes

Acknowledgements

The author is grateful to Professor Röckner for insightful discussions and constant encouragement. This work is supported by NSFC (No. 11501362). Financial support through SFB1283 at Bielefeld University is also gratefully acknowledged.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiChina

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