The cubic nonlinear Dirac equation

Abstract

We present some results obtained in collaboration with prof. Piero D'Ancona concerning global existence for the 3D cubic non linear massless Dirac equation with a potential for small initial data in $H^1$ with slight additional assumptions. The new crucial tool is given by the proof of some refined endpoint Strichartz estimates.Comment: 10 pages; Days on PDEs 2012, Biarritz (France). arXiv admin note: text overlap with arXiv:1103.401