Renormalization of Generalized KPZ equation

TL;DR

This paper applies Renormalization Group techniques to establish local well-posedness for a generalized KPZ equation, addressing divergence issues with counter terms in stochastic hydrodynamics.

Contribution

It introduces a novel renormalization approach to handle divergences in a generalized KPZ equation, extending previous methods in stochastic PDE analysis.

Findings

Proves local well-posedness of the generalized KPZ equation.

Identifies necessary counter terms diverging with cutoff.

Provides a rigorous renormalization framework for stochastic PDEs.

Abstract

We use Renormalization Group to prove local well posedness for a generalized KPZ equation introduced by H. Spohn in the context of stochastic hydrodynamics. The equation requires the addition of counter terms diverging with a cutoff $\epsilon$ as $\epsilon^{-1}$ and $\log\epsilon^{-1}$.