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 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.
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}
}