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.

arXiv comment78 pages

References in corpus (8)

• A theory of regularity structures
• Random data Cauchy theory for supercritical wave equations I: Local theory
• Random data Cauchy theory for supercritical wave equations II : A global existence result
• Global regularity for the Maxwell-Klein-Gordon equation with small critical Sobolev norm in high dimensions
• Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation
• Almost sure scattering for the radial energy critical nonlinear wave equation in three dimensions
• Global well-posedness for the Maxwell-Klein Gordon equation in 4+1 dimensions. Small energy
• Hodge-Teichmueller planes and finiteness results for Teichmueller curves

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