Large time well posedness for a Dirac--Klein-Gordon system
Federico Cacciafesta, Anne-Sophie de Suzzoni, Long Meng, J\'er\'emy, Sok
TL;DR
This paper establishes well-posedness for a coupled Dirac--Klein-Gordon system modeling a relativistic Helium atom, introducing new Strichartz estimates for time-dependent Dirac perturbations.
Contribution
It provides the first well-posedness results for this coupled system and develops novel Strichartz estimates for time-dependent Dirac equations.
Findings
Proved well-posedness of the Dirac--Klein-Gordon system.
Developed new Strichartz estimates for time-dependent Dirac operators.
Model serves as a toy for relativistic Helium atom analysis.
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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