Absolute continuity of the solution to the stochastic Burgers equation

TL;DR

This paper proves the existence and regularity of the probability density for solutions to a class of stochastic partial differential equations, including the stochastic Burgers equation, using an elementary fractional integration method.

Contribution

It introduces a simple fractional integration by parts approach to establish density regularity for solutions of parabolic SPDEs, including the stochastic Burgers equation.

Findings

Existence of the solution's density

Besov regularity of the density

Applicable to unbounded domains

Abstract

We prove the existence and the Besov regularity of the density of the solution to a general parabolic SPDE which includes the stochastic Burgers equation on an unbounded domain. We use an elementary approach based on the fractional integration by parts.