On a forward-backward stochastic system associated to the Burgers equation

TL;DR

This paper presents a probabilistic method to construct regular solutions for the periodic forced Burgers equation using a forward-backward stochastic system, offering a new perspective on solving this nonlinear PDE.

Contribution

It introduces a novel probabilistic framework linking the Burgers equation solutions to forward-backward stochastic systems, advancing the analytical tools available for such equations.

Findings

Constructed $H^s$-regular solutions probabilistically

Linked solutions to a forward-backward stochastic system

Provided a new approach for analyzing the Burgers equation

Abstract

We describe a probabilistic construction of $H^s$-regular solutions for the spatially periodic forced Burgers equation by using a characterization of this solution through a forward-backward stochastic system.