Subcritical approximations to stochastic defocusing mass-critical nonlinear Schr\"odinger equation on $\mathbb{R}$

Chenjie Fan; Weijun Xu

Subcritical approximations to stochastic defocusing mass-critical nonlinear Schr\"odinger equation on $\mathbb{R}$

Analysis of PDEs 2018-10-23 v1 Probability

Authors: Chenjie Fan , Weijun Xu

Abstract

We show robustness of various truncated and subcritical approximations to the stochastic defocusing mass-critical nonlinear Schr\"odinger equation (NLS) in dimension $d=1$ , whose solution was constructed in [FX18] with one particular such approximation. The key ingredient in the proof is a uniform bound of the solutions to the family of deterministic mass-subcritical defocusing NLS.

Keywords

stochastic nonlinear schrödinger equation mass-critical subcritical approximations uniform bound robustness

Cite

@article{arxiv.1810.09407,
  title  = {Subcritical approximations to stochastic defocusing mass-critical nonlinear Schr\"odinger equation on $\mathbb{R}$},
  author = {Chenjie Fan and Weijun Xu},
  journal= {arXiv preprint arXiv:1810.09407},
  year   = {2018}
}

Comments

23 pages. The material of this article is contained in arXiv:1807.04402. The other part of arXiv:1807.04402 has been combined with arXiv:1803.03257 to form another new article arXiv:1810.07925. Only the current paper and arXiv:1810.07925 will be submitted for journal publication

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