English

Solution to the stochastic Schr\"odinger equation on the full space

Probability 2017-07-21 v1 Analysis of PDEs

Abstract

We here show how the methods recently applied by [DW16] to solve the stochastic nonlinear Schr\"odinger equation on T2\mathbb{T}^2 can be enhanced to yield solutions on R2\mathbb{R}^2 if the non-linearity is weak enough. We prove that the solutions remains localized on compact time intervals which allows us to apply energy methods on the full space.

Keywords

Cite

@article{arxiv.1707.06431,
  title  = {Solution to the stochastic Schr\"odinger equation on the full space},
  author = {Arnaud Debussche and Jörg Martin},
  journal= {arXiv preprint arXiv:1707.06431},
  year   = {2017}
}
R2 v1 2026-06-22T20:52:43.127Z