On the stochastic nonlinear Schr\"odinger equations with non-smooth additive noise

TL;DR

This paper investigates stochastic nonlinear Schrödinger equations with rougher additive noise, establishing a simple method to prove the existence of unique local solutions despite the increased noise irregularity.

Contribution

The authors introduce a novel approach leveraging dispersive estimates to handle non-smooth stochastic forcing in Schrödinger equations, extending previous results.

Findings

Established local existence and uniqueness of solutions with rougher noise

Developed a simplified argument using dispersive estimates

Extended the class of stochastic forcing considered in the literature

Abstract

We study the stochastic nonlinear Schr\"odinger equations with additive stochastic forcing. By using the dispersive estimate, we present a simple argument, constructing a unique local-in-time solution with rougher stochastic forcing than those considered in the literature.