PUB - Publikationen an der Universität Bielefeld

This paper is devoted to the study of noise effects on blow-up solutions to stochastic nonlinear Schrodinger 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 < infinity. Moreover, in the case of spatially independent noise, the explosion even can be prevented with high probability on the whole time interval [0, infinity). The noise effects obtained here are completely different from those in the conservative case studied in [5]. (C) 2017 Elsevier Inc. All rights reserved.