The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates

We consider the stochastic NLS with linear multiplicative noise in L2(Rd) and prove the existence and uniqueness of a global solution in the subcritical and a local solution in the critical case, respectively. In particular, we relax the regularity assumptions on the noise from Barbu, R¨ockner and Zhang (Stochastic Nonlinear Schr¨odinger Equations with Linear Multiplicative Noise: Rescaling Approach. Journal of Nonlinear Science 24(3):383-409,2014). The proof is based on deterministic and stochastic Strichartz estimates.