English

Local well-posedness for the nonlinear Dirac equation in two space dimensions

Analysis of PDEs 2014-02-06 v6

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.

Keywords

Cite

@article{arxiv.1303.1699,
  title  = {Local well-posedness for the nonlinear Dirac equation in two space dimensions},
  author = {Hartmut Pecher},
  journal= {arXiv preprint arXiv:1303.1699},
  year   = {2014}
}

Comments

21 pages. This is (almost) identical with version 1. The versions 2-4 contain an error in the proof of Proposition 2.1

R2 v1 2026-06-21T23:38:13.097Z