Strong solution of the stochastic Burgers equation

TL;DR

This paper introduces a pathwise solution concept for the stochastic Burgers equation, extending the classical Cole-Hopf solution using distribution theory and regularization techniques.

Contribution

It provides a new framework for solving the stochastic Burgers equation that includes the Cole-Hopf solution as a special case.

Findings

Established a pathwise solution concept for the stochastic Burgers equation.

Unified the Cole-Hopf solution within this new framework.

Utilized regularization and distribution theory methods.

Abstract

This work introduces a pathwise notion of solution for the stochastic Burgers equation, in particular, our approach encompasses the Cole-Hopf solution. The developments are based on regularization arguments from the theory of distributions.