Global well-posedness for the mass-critical stochastic nonlinear Schrödinger equation on $\mathbb{R}$: general $L^2$ data

Abstract

We continue our study for the stochastic defocusing mass crtical nonlinear Schrödinger equation with conservative multiplicative noise, and show that it is globally well-posed for arbitrary initial data in $L_{\omega }^{\infty }{L}_x^2$. The main ingredients are several stability type results for deterministic (modified) NLS, which have their own interest. We also give some results on other stochastic NLS type models.

32 pages. All comments are welcome