Global well-posedness for the Maxwell-Klein Gordon equation in 4+1   dimensions. Small energy
  We prove that the critical Maxwell-Klein Gordon equation on R4+1 is globally well-posed for smooth initial data which are small in the energy. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of energy. 
Joachim Krieger, Jacob Sterbenz, Daniel Tataru
math.AP