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The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates

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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.

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Authors and Affiliations

  1. Institute for Analysis, Karlsruhe Institute for Technology (KIT), 76128, Karlsruhe, Germany

    Fabian Hornung

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  1. Fabian Hornung
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Correspondence to Fabian Hornung.

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Hornung, F. The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates. J. Evol. Equ. 18, 1085–1114 (2018). https://doi.org/10.1007/s00028-018-0433-7

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  • DOI: https://doi.org/10.1007/s00028-018-0433-7

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