Null structure and almost optimal local well-posedness of the   Dirac-Klein-Gordon system
  We prove almost optimal local well-posedness for the coupled   Dirac-Klein-Gordon (DKG) system of equations in 1+3 dimensions.   The proof relies on the null structure of the system, combined with bilinear spacetime estimates of Klainerman-Machedon type.   It has been known for some time that the Klein-Gordon part of the system has a null structure; here we uncover an additional null structure in the Dirac equation, which cannot be seen directly, but appears after a duality argument. 
Piero D'Ancona, Damiano Foschi, and Sigmund Selberg