We prove that the critical Maxwell–Klein–Gordon equation on is globally well-posed for smooth initial data which are small in the energy norm. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of energy.
Joachim Krieger. Jacob Sterbenz. Daniel Tataru. "Global well-posedness for the Maxwell–Klein–Gordon equation in dimensions: Small energy." Duke Math. J. 164 (6) 973 - 1040, 15 April 2015. https://doi.org/10.1215/00127094-2885982