Global dynamics of the $2d$ NLS with white noise potential and generic polynomial nonlinearity
Probability
2023-07-05 v1 Analysis of PDEs
Abstract
Using an approach introduced by Hairer-Labb\' e we construct a unique global dynamics for the NLS on with a white noise potential and an arbitrary polynomial nonlinearity. We build the solutions as a limit of classical solutions (up to a phase shift) of the same equation with smoothed potentials. This is an improvement on previous contributions of us and Debussche-Weber dealing with quartic nonlinearities and cubic nonlinearities respectively.
Keywords
Cite
@article{arxiv.2204.03280,
title = {Global dynamics of the $2d$ NLS with white noise potential and generic polynomial nonlinearity},
author = {N. Tzvetkov and N. Visciglia},
journal= {arXiv preprint arXiv:2204.03280},
year = {2023}
}