@article{Miao2025, 
author = {Lijun Miao and Jingwei Yu and Linlin Qiu},
title = {On global existence for the stochastic nonlinear Schrödinger equation with time-dependent linear loss/gain},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {6},
pages = {3571-3583},
keywords = {stochastic nonlinear Schrödinger equation, global existence, time-dependent loss/gain, additive noise, energy space},
url = {https://www.sciopen.com/article/10.3934/era.2025159},
doi = {10.3934/era.2025159},
abstract = {This paper was focused on global existence for the stochastic nonlinear Schrödinger equation with time-dependent loss/gain, which read        i    d  u  +  (  Δ  u  +  λ      |    u            |        α    u  +  i  a  (  t  )  u  )  d  t  =  d  W. We proved the global existence and uniqueness of the solution in        H    1    (            R        N    ) through the uniform boundedness of the momentum and energy functionals. The global existence result of the solution for this type of equation depended on the ranges of time-dependent loss/gain coefficient.}
}