Probabilistic Small Data Global Well-Posedness of the Energy-Critical Maxwell–Klein–Gordon Equation
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Author(s)
Krieger, Joachim
Lührmann, Jonas
Staffilani, Gigliola
Date Issued
July 17, 2023
Publisher
Springer Berlin Heidelberg
Citation
Archive for Rational Mechanics and Analysis. 2023 Jul 17;247(4):68
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00205-023-01900-w
