Local well-posedness for the nonlinear Dirac equation in two space dimensions
arXiv:1303.1699
Abstract
The Cauchy problem for the cubic nonlinear Dirac equation in two space dimensions is locally well-posed for data in H^s for s > 1/2. The proof given in spaces of Bourgain-Klainerman-Machedon type relies on the null structure of the nonlinearity as used by d'Ancona-Foschi-Selberg for the Dirac-Klein-Gordon system before and bilinear Strichartz type estimates for the wave equation by Selberg and Foschi-Klainerman.
21 pages. This is (almost) identical with version 1. The versions 2-4 contain an error in the proof of Proposition 2.1