Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation
We prove global regularity, scattering and a priori bounds for the energy critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge on (1+4)-dimensional Minkowski space. The proof is based upon a modified Bahouri-Gerard profile decomposition  and a concentration compactness/rigidity argument by Kenig-Merle , following the method developed by the first author and Schlag  in the context of critical wave maps. This is a preliminary version of the final paper.
Record created on 2015-04-01, modified on 2016-08-11