# Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise

## TL;DR

This paper studies the spatial Sobolev regularity of solutions to stochastic Burgers equations with additive trace class noise, using bootstrap methods and nonlinearity analysis.

## Contribution

It provides new insights into the regularity properties of solutions to stochastic Burgers equations with trace class noise.

## Key findings

- Established Sobolev regularity results for mild solutions.
- Analyzed the impact of nonlinearity on solution regularity.
- Combined bootstrap techniques with nonlinearity analysis.

## Abstract

In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combination of suitable bootstrap-type arguments and a detailed analysis of the nonlinearity in the equation.