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Journal of Evolution Equations

, Volume 18, Issue 3, pp 1085–1114 | Cite as

The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates

  • Fabian HornungEmail author
Article

Abstract

We consider the stochastic NLS with nonlinear Stratonovich noise for initial values in \({L^2({\mathbb {R}^d})}\) and prove local existence and uniqueness of a mild solution for subcritical and critical nonlinearities. The proof is based on deterministic and stochastic Strichartz estimates. In the subcritical case we prove that the solution is global, if we impose an additional assumption on the nonlinear noise.

Keywords

Nonlinear Schrödinger equation Stratonovich noise Stochastic Strichartz estimates 

Mathematics Subject Classification

35Q41 35R60 60H15 60H30 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for AnalysisKarlsruhe Institute for Technology (KIT)KarlsruheGermany

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