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arXiv · 2110.08624

Large time well posedness for a Dirac--Klein-Gordon system

Federico Cacciafesta·Anne-Sophie de Suzzoni·Long Meng·Jérémy Sok
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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.

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Federico Cacciafesta, Anne-Sophie de Suzzoni, Long Meng, Jérémy Sok. 2021-10-16. Large time well posedness for a Dirac--Klein-Gordon system. https://arxiv.org/abs/2110.08624

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