The Allen-Cahn equation with generic initial datum
Analysis of PDEs
2022-01-24 v1 Probability
Abstract
We consider the Allen-Cahn equation with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets of the Bargmann-Fock Gaussian field, which then evolve according to mean curvature flow.
Cite
@article{arxiv.2201.08426,
title = {The Allen-Cahn equation with generic initial datum},
author = {Martin Hairer and Khoa Lê and Tommaso Rosati},
journal= {arXiv preprint arXiv:2201.08426},
year = {2022}
}