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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2407.03554 |
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| _version_ | 1866914342579994624 |
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| author | Salvi, Tony |
| author_facet | Salvi, Tony |
| contents | We study a 1-parameter family (Aλ, Φλ)λ of multi-phase high frequency solutions to Klein-Gordon-Maxwell equations in Lorenz gauge in the (3+1)-dimensional Minkowski spacetime. This family is based on an initial ansatz. We prove that for λ small enough the family of solutions exists on an interval uniform in λ only function of the initial ansatz. These solutions are close to an approximate solution constructed by geometric optics. The initial ansatz needs to be regular enough, to satisfy a polarization condition and to satisfy the constraints for Maxwell null-transport in Lorenz gauge, but there is no need for smallness of any kind. The phases need to interact in a coherent way. We also observe that the limit (A0, Φ0) is not solution to Klein-Gordon-Maxwell equations but to a Klein-Gordon-Maxwell null-transport type system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-phase high frequency solutions to Klein-Gordon-Maxwell equations in Lorenz gauge in (3+1) Minkowski spacetime Salvi, Tony Analysis of PDEs We study a 1-parameter family (Aλ, Φλ)λ of multi-phase high frequency solutions to Klein-Gordon-Maxwell equations in Lorenz gauge in the (3+1)-dimensional Minkowski spacetime. This family is based on an initial ansatz. We prove that for λ small enough the family of solutions exists on an interval uniform in λ only function of the initial ansatz. These solutions are close to an approximate solution constructed by geometric optics. The initial ansatz needs to be regular enough, to satisfy a polarization condition and to satisfy the constraints for Maxwell null-transport in Lorenz gauge, but there is no need for smallness of any kind. The phases need to interact in a coherent way. We also observe that the limit (A0, Φ0) is not solution to Klein-Gordon-Maxwell equations but to a Klein-Gordon-Maxwell null-transport type system. |
| title | Multi-phase high frequency solutions to Klein-Gordon-Maxwell equations in Lorenz gauge in (3+1) Minkowski spacetime |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.03554 |