Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation
Analysis of PDEs
2015-11-23 v3
Abstract
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 [1] and a concentration compactness/rigidity argument by Kenig-Merle [10], following the method developed by the first author and Schlag [20] in the context of critical wave maps.
Cite
@article{arxiv.1503.09101,
title = {Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation},
author = {Joachim Krieger and Jonas Luhrmann},
journal= {arXiv preprint arXiv:1503.09101},
year = {2015}
}
Comments
160 pages. Minor revisions. To appear in Annals of PDE