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 H 1 , 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 < T < ∞ . Moreover, in the case of spatially independent noise, the explosion even can be prevented with high probability on the whole time interval [ 0 , ∞ ) . The noise effects obtained here are completely different from those in the conservative case studied in [5] . [ABSTRACT FROM AUTHOR]