The cubic Dirac equation: Small initial data in $H^{\frac12}(\mathbb{R}^2)$
Analysis of PDEs
2016-03-31 v3
Abstract
Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space is established. The proof is based on a sharp endpoint Strichartz estimate for the Klein-Gordon equation in dimension , which is captured by constructing an adapted systems of coordinate frames.
Cite
@article{arxiv.1501.06874,
title = {The cubic Dirac equation: Small initial data in $H^{\frac12}(\mathbb{R}^2)$},
author = {Ioan Bejenaru and Sebastian Herr},
journal= {arXiv preprint arXiv:1501.06874},
year = {2016}
}
Comments
58 pages. Notation, setup and general reductions are adopted from our work arXiv:1310.5280, where we address the same problem in the 3d case. The analysis is significantly different. v3: 56 pages, Correction of the definitions of the sets \Lambda_{k,\omega} and \Lambda_{k,\omega}^{j}