Stochastic nonlinear Schrödinger equations: No blow-up in the non-conservative case

This paper is devoted to the study of noise effects on blow-up solutions to stochastic nonlinear Schrödinger equations. It is a continuation of our recent work [2], where the (local) well-posedness is established in H1, also in the non-conservative critical case. Here we prove that in the non-conservative focusing mass-(super)critical case, by adding a large multiplicative Gaussian noise, with high probability one can prevent the blow-up on any given bounded time interval [0,T], 0