Global Solution and Blow-up of the Stochastic Nonlinear Schrödinger system

Abstract

We study the stochastic Nonlinear Schrödinger system with multiplicative white noise in energy space $H^1$. 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 $L^2$ norm of initial value is small enough. In addition, we study the blow-up phenomenon and give a sharp criteria.

References in corpus (2)

• Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrodinger system
• Blow-up behavior of ground states for a nonlinear Schrödinger system with attractive and repulsive interactions