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research article
Probabilistic small data global Well-Posedness of the energy-critical Maxwell-Klein-Gordon equation
October 19, 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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KLS(24).pdf
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