A flow approach to the generalized KPZ equation
arXiv:2402.03101
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.
Adaptation of the proof to the case of a rough initial condition