English

Two dimensional nonlinear Schr\"odinger equation with spatial white noise potential and fourth order nonlinearity

Analysis of PDEs 2020-06-16 v1 Mathematical Physics math.MP

Abstract

We consider NLS on \T2\T^2 with multiplicative spatial white noise and nonlinearity between cubic and quartic. We prove global existence, uniqueness and convergence almost surely of solutions to a family of properly regularized and renormalized approximating equations. In particular we extend a previous result by A. Debussche and H. Weber available in the cubic and sub-cubic setting.

Keywords

Cite

@article{arxiv.2006.07957,
  title  = {Two dimensional nonlinear Schr\"odinger equation with spatial white noise potential and fourth order nonlinearity},
  author = {Nikolay Tzvetkov and Nicola Visciglia},
  journal= {arXiv preprint arXiv:2006.07957},
  year   = {2020}
}
R2 v1 2026-06-23T16:18:53.057Z