Modified scattering for the three dimensional Maxwell-Dirac system
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917428286455808 |
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| author | Herr, Sebastian Ifrim, Mihaela Spitz, Martin |
| author_facet | Herr, Sebastian Ifrim, Mihaela Spitz, Martin |
| contents | In this work we prove global well-posedness for the massive Maxwell-Dirac system in the Lorenz gauge in $\mathbb{R}^{1+3}$, for small, sufficiently smooth and decaying initial data, as well as modified scattering for the solutions. Heuristically we exploit the close connection between the massive Maxwell-Dirac and the wave-Klein-Gordon equations, while developing a novel approach which applies directly at the level of the Dirac equations. The modified scattering result follows from a precise description of the asymptotic behavior of the solutions inside the light cone, which we derive via the method of testing with wave packets of Ifrim-Tataru. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modified scattering for the three dimensional Maxwell-Dirac system Herr, Sebastian Ifrim, Mihaela Spitz, Martin Analysis of PDEs Classical Analysis and ODEs 81R20, 35Q61, 35Q41 In this work we prove global well-posedness for the massive Maxwell-Dirac system in the Lorenz gauge in $\mathbb{R}^{1+3}$, for small, sufficiently smooth and decaying initial data, as well as modified scattering for the solutions. Heuristically we exploit the close connection between the massive Maxwell-Dirac and the wave-Klein-Gordon equations, while developing a novel approach which applies directly at the level of the Dirac equations. The modified scattering result follows from a precise description of the asymptotic behavior of the solutions inside the light cone, which we derive via the method of testing with wave packets of Ifrim-Tataru. |
| title | Modified scattering for the three dimensional Maxwell-Dirac system |
| topic | Analysis of PDEs Classical Analysis and ODEs 81R20, 35Q61, 35Q41 |
| url | https://arxiv.org/abs/2406.02460 |