Endpoint estimates and global existence for the nonlinear Dirac equation   with potential
  We prove endpoint estimates with angular regularity for the wave and Dirac equations perturbed with a small potential. The estimates are applied to prove global existence for the cubic Dirac equation perturbed with a small potential, for small initial $H^{1}$ data with additional angular regularity. This implies in particular global existence in the critical energy space $H^{1}$ for small radial data. 
Federico Cacciafesta and Piero D'Ancona
math.AP math-ph math.MP