Large time well posedness for a Dirac--Klein-Gordon system
Analysis of PDEs
2021-10-19 v1
Abstract
In this paper we prove well posedness for a system coupling a nonlinear Dirac with a Klein-Gordon equation that represents a toy model for the Helium atom with relativistic corrections: the wave function of the electrons interacts with an electric field generated by a nucleus with a given charge density. One of the main ingredients we need is a new family of Strichartz estimates for time dependent perturbations of the Dirac equation: these represent a result of independent interest.
Cite
@article{arxiv.2110.08624,
title = {Large time well posedness for a Dirac--Klein-Gordon system},
author = {Federico Cacciafesta and Anne-Sophie de Suzzoni and Long Meng and Jérémy Sok},
journal= {arXiv preprint arXiv:2110.08624},
year = {2021}
}
Comments
32 pages