Long time behavior of stochastic NLS with a small multiplicative noise

Abstract

We prove the global space-time bound for the mass critical nonlinear Schrödinger equation perturbed by a small multiplicative noise in dimension three. The associated scattering behavior are also obtained. We also prove a global Strichartz space-time bound for the linear stochastic model, which is new itself and serves a prototype model for the nonlinear case. The proof combines techniques from \cite{fan2018global}, \cite{fan2020long} as well as local smoothing estimates for linear Schrödinger operators.

arXiv commentWe include the scattering behavior in this revision and all non endpoint Strichartz type bound are now included for nonlinear model. 28 pages, no figures, all comments are welcome

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