Global finite energy solutions of the Maxwell-scalar field system on the Einstein cylinder

2025/07/22 by Jean-Philippe Nicolas, Grigalius Taujanskas, Nicolas, Jean-Philippe +1 · 1 voice
Physics and Astronomy · Mathematics · #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2507.16750

Abstract

We prove the existence and uniqueness of global finite energy solutions of the Maxwell-scalar field system in Lorenz gauge on the Einstein cylinder. Our method is a combination of a conformal patching argument, the finite energy existence theorem in Lorenz gauge on Minkowski space of Selberg and Tesfahun, a careful localization of finite energy data, and null form estimates of Foschi-Klainerman type. Although we prove that the energy-carrying components of the solution maintain regularity, due to the incompleteness of the null structure in Lorenz gauge and the nature of our foliation-change arguments we find small losses of regularity in both the scalar field and the potential.

Citations

• Space‐time estimates for null forms and the local existence theorem
• Smoothing estimates for null forms and applications

Discussions

• If you ever want to make an scientist really happy, cite a paper of theirs that nobody paid attention to for decades, and call it "pioneering". Great new global existence results for classical Yang-Mi [bsky, 43 points, 2 comments]

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