The aim of these notes is to provide an overview of the ideas in the recent proof of global well-posedness for the massive Maxwell-Dirac system in the Lorenz gauge in , for small and decaying initial data of limiting regularity. The result also includes an in-depth study of the asymptotic dynamics of the global solutions, which can be described as modified scattering. While heuristically we exploit the close connection between the massive Maxwell-Dirac and the wave-Klein-Gordon equations, for the proof of the results we develop 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 is derived via the method of testing with wave packets of Ifrim-Tataru.
Sebastian Herr 1 ; Mihaela Ifrim 2 ; Martin Spitz 1
@article{SLSEDP_2024-2025____A9_0,
author = {Sebastian Herr and Mihaela Ifrim and Martin Spitz},
title = {Global dynamics for the {3D} {Maxwell-Dirac} system},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:20},
pages = {1--21},
year = {2024-2025},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
doi = {10.5802/slsedp.182},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.182/}
}
TY - JOUR AU - Sebastian Herr AU - Mihaela Ifrim AU - Martin Spitz TI - Global dynamics for the 3D Maxwell-Dirac system JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:20 PY - 2024-2025 SP - 1 EP - 21 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.182/ DO - 10.5802/slsedp.182 LA - en ID - SLSEDP_2024-2025____A9_0 ER -
%0 Journal Article %A Sebastian Herr %A Mihaela Ifrim %A Martin Spitz %T Global dynamics for the 3D Maxwell-Dirac system %J Séminaire Laurent Schwartz — EDP et applications %Z talk:20 %D 2024-2025 %P 1-21 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.182/ %R 10.5802/slsedp.182 %G en %F SLSEDP_2024-2025____A9_0
Sebastian Herr; Mihaela Ifrim; Martin Spitz. Global dynamics for the 3D Maxwell-Dirac system. Séminaire Laurent Schwartz — EDP et applications (2024-2025), Exposé no. 20, 21 p.. doi: 10.5802/slsedp.182
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