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arXiv · 2507.16750

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

Jean-Philippe Nicolas·Grigalius Taujanskas
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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.

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Jean-Philippe Nicolas, Grigalius Taujanskas. 2025-07-22. Global finite energy solutions of the Maxwell-scalar field system on the Einstein cylinder. https://arxiv.org/abs/2507.16750

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