Global Solution and Blow-up of the Stochastic Nonlinear Schr\"{o}dinger system
Analysis of PDEs
2019-12-12 v2
Abstract
We study the stochastic Nonlinear Schr\"{o}dinger system with multiplicative white noise in energy space . Based on deterministic and stochastic Strichartz estimates, we prove the local well-posedness and uniqueness of mild solution. Then we prove the global well-posedness in the mass subcritical case and the defocusing case. For the mass subcritical case, we also investigate the global existence when the norm of initial value is small enough. In addition, we study the blow-up phenomenon and give a sharp criteria.
Keywords
Cite
@article{arxiv.1912.01488,
title = {Global Solution and Blow-up of the Stochastic Nonlinear Schr\"{o}dinger system},
author = {Qi Zhang and Jinqiao Duan and Yong Chen},
journal= {arXiv preprint arXiv:1912.01488},
year = {2019}
}