A flow approach to the generalized KPZ equation
Probability
2025-04-23 v5 Analysis of PDEs
Abstract
We show that the flow approach of Duch [Duc21] can be adapted to prove local well-posedness for the generalized Kardar-Parisi-Zhang equation. The key step is to extend the flow approach so that it can accommodate semi-linear equations involving smooth, non-polynomial, functions of the solution - this is accomplished by introducing coordinates for the flow built out of elementary differentials.
Keywords
Cite
@article{arxiv.2402.03101,
title = {A flow approach to the generalized KPZ equation},
author = {Ajay Chandra and Léonard Ferdinand},
journal= {arXiv preprint arXiv:2402.03101},
year = {2025}
}
Comments
Adaptation of the proof to the case of a rough initial condition