Generalized solutions of the stochastic Burgers equation

TL;DR

This paper introduces a new weak solution concept for the conservative stochastic Burgers equation applicable in any dimension, extending classical solutions and addressing equations lacking distributional solutions.

Contribution

It proposes a novel weak solution framework for the stochastic Burgers equation that generalizes existing concepts to higher dimensions.

Findings

Defines a new weak solution concept for stochastic Burgers equations

Ensures the solution reduces to classical in one dimension

Provides a foundation for analyzing equations without distributional solutions

Abstract

We introduce a new concepts of weak solution for the conservative stochastic Burgers equation in any dimension. The definition is based on weak solution concepts introduced by various authors in order to make sense of equations which do not solutions in the sense of distributions. In one dimension the solution reduces to the classical distributional solution of the 1--D stochastic Burgers equation.