# Well-posedness of a gauge-covariant wave equation with space-time white noise forcing

## TL;DR

This paper introduces a new stochastic gauge-covariant wave equation model with space-time white noise and proves its global well-posedness in the Lorenz gauge, while also identifying obstructions to similar equations.

## Contribution

It presents the first probabilistic well-posedness result for a 2D gauge-covariant wave equation with white noise and highlights challenges in extending to Maxwell-Klein-Gordon equations.

## Key findings

- Probabilistic global well-posedness in Lorenz gauge.
- Failure of probabilistic null-form estimate.
- Potential obstructions for stochastic Maxwell-Klein-Gordon equations.

## Abstract

We first introduce a new model for a two-dimensional gauge-covariant wave equation with space-time white noise. In our main theorem, we obtain the probabilistic global well-posedness of this model in the Lorenz gauge. Furthermore, we prove the failure of a probabilistic null-form estimate, which exposes a potential obstruction towards the probabilistic well-posedness of a stochastic Maxwell-Klein-Gordon equation.