Large Time Behavior of the Klein-Gordon-Schrödinger system
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913890002010112 |
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| author | You, Chanjin |
| author_facet | You, Chanjin |
| contents | We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schrödinger system in three dimensions. The system consists of coupled semilinear Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large Time Behavior of the Klein-Gordon-Schrödinger system You, Chanjin Analysis of PDEs Mathematical Physics We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schrödinger system in three dimensions. The system consists of coupled semilinear Schrödinger 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. |
| title | Large Time Behavior of the Klein-Gordon-Schrödinger system |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2506.09863 |