Well-posedness of a gauge-covariant wave equation with space-time white noise forcing
arXiv:2302.14271 · doi:10.2140/pmp.2025.6.139
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.
53 pages. Corrected typographical errors and incorporated referees' suggestions
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