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

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