# Probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation.

@article{Krieger2020ProbabilisticSD, title={Probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation.}, author={Joachim Krieger and Jonas Luhrmann and Gigliola Staffilani}, journal={arXiv: Analysis of PDEs}, year={2020} }

We establish probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge for scaling super-critical random initial data. The proof relies on an induction on frequency procedure and a modified linear-nonlinear decomposition furnished by a delicate "probabilistic" parametrix construction. This is the first global existence result for a geometric wave equation for random initial data at scaling super-critical regularity.

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