# Existence, uniqueness, and numerical approximations for stochastic Burgers equations

## TL;DR

This paper establishes existence, uniqueness, regularity, and numerical approximation results for stochastic PDEs with non-globally monotone nonlinearities, including the stochastic Burgers equations with white noise, using explicit schemes.

## Contribution

It provides a comprehensive framework for analyzing and approximating solutions to complex SPDEs with non-globally monotone nonlinearities, including new convergence results.

## Key findings

- Almost sure convergence of the numerical scheme to the mild solutions
- Strong convergence results for the approximation scheme
- Application to stochastic Burgers equations with space-time white noise

## Abstract

In this paper we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existent fully explicit space-time discrete approximation scheme and, in particular, the fact that it satisfies suitable a priori estimates. As a byproduct we obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the paper to the stochastic Burgers equations with space-time white noise.