The logarithmic Schr{\"o}dinger equation with spatial white noise on the full space
Analysis of PDEs
2023-08-31 v1 Probability
Abstract
We solve the Schr{\"o}dinger equation with logarithmic nonlinearity and multiplicative spatial white noise on R d with d 2. Because of the nonlinearity, the regularity structures and the paracontrolled calculus can not be used. To solve the equation, we rely on an exponential transform that has proven useful in the context of other singular SPDEs.
Keywords
Cite
@article{arxiv.2308.15814,
title = {The logarithmic Schr{\"o}dinger equation with spatial white noise on the full space},
author = {Quentin Chauleur and Antoine Mouzard},
journal= {arXiv preprint arXiv:2308.15814},
year = {2023}
}