  This article is devoted to the mass-less energy critical Maxwell-Klein-Gordon
system in 4+1 dimensions. In earlier work of the second author, joint with
Krieger and Sterbenz, we have proved that this problem has global
well-posedness and scattering in the Coulomb gauge for small initial data. This
article is the second of a sequence of three papers of the authors, whose goal
is to show that the same result holds for data with arbitrarily large energy.
Our aim here is to show that large data solutions persist for as long as one
has small energy dispersion; hence failure of global well-posedness must be
accompanied with a non-trivial energy dispersion.

Analysis of PDEs