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arXiv · 2506.09863

Large Time Behavior of the Klein-Gordon-Schr\"{o}dinger system

Chanjin You
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Abstract

We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schr\"{o}dinger system in three dimensions. The system consists of coupled semilinear Schr\"{o}dinger and Klein-Gordon equations with quadratic nonlinearities. This model is motivated by the study of plasma oscillations arising from the Hartree equation near a translation-invariant equilibrium with the Coulomb potential. Our proof relies on the space-time resonance method. The main difficulty comes from the two dimensional space-time resonant set and the absence of null form structure.

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Chanjin You. 2025-06-11. Large Time Behavior of the Klein-Gordon-Schr\"{o}dinger system. https://arxiv.org/abs/2506.09863

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