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

Abstract

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.

78 pages

References in corpus (2)

• Random data Cauchy theory for supercritical wave equations I: Local theory
• Random data Cauchy theory for supercritical wave equations II : A global existence result

Cited by in corpus (2)

• Well-posedness of a gauge-covariant wave equation with space-time white noise forcing
• Local well-posedness of subcritical non-linear heat equations with Gaussian initial data