Modified Scattering for the Three Dimensional Maxwell-Dirac System
Abstract
Abstract In this work we prove global well-posedness for the massive Maxwell-Dirac system in the Lorenz gauge in $$\mathbb {R}^{1+3}$$ R 1 + 3 , for small, sufficiently smooth and decaying initial data, as well as modified scattering for the solutions. Heuristically we exploit the close connection between the massive Maxwell-Dirac and the wave-Klein-Gordon equations, while developing a novel approach which applies directly at the level of the Dirac equations. The modified scattering result follows from a precise description of the asymptotic behavior of the solutions inside the light cone, which we derive via the method of testing with wave packets of Ifrim-Tataru.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods in inverse problems
Gas Dynamics and Kinetic Theory
Publication details
- Journal / source
- Annals of PDE
- Publisher
- Springer Science and Business Media LLC
- Volume
- 12
- Issue
- 1
- Publication date
- 22 April 2026
- Language
- EN