The global dynamics for the Maxwell-Dirac system
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917742701969408 |
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| author | Cho, Yonggeun Lee, Kiyeon |
| author_facet | Cho, Yonggeun Lee, Kiyeon |
| contents | In this paper, we study the (1+3) dimensional massive Maxwell-Dirac system in the context of global existence and asymptotic behavior of solutions under the Lorenz gauge condition, as well as the modified and linear scattering phenomena for the Dirac spinor and the electromagnetic potential, respectively. We employ a vector fields energy method combined with a detailed analysis of the space-time resonance argument. This approach allows us to establish decay estimates and energy bounds crucial for proving the main theorems. Especially, we provide the explicit phase correction arising from the strong nonlinear resonances. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_18887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The global dynamics for the Maxwell-Dirac system Cho, Yonggeun Lee, Kiyeon Analysis of PDEs 35Q41, 35Q55, 35Q40 In this paper, we study the (1+3) dimensional massive Maxwell-Dirac system in the context of global existence and asymptotic behavior of solutions under the Lorenz gauge condition, as well as the modified and linear scattering phenomena for the Dirac spinor and the electromagnetic potential, respectively. We employ a vector fields energy method combined with a detailed analysis of the space-time resonance argument. This approach allows us to establish decay estimates and energy bounds crucial for proving the main theorems. Especially, we provide the explicit phase correction arising from the strong nonlinear resonances. |
| title | The global dynamics for the Maxwell-Dirac system |
| topic | Analysis of PDEs 35Q41, 35Q55, 35Q40 |
| url | https://arxiv.org/abs/2406.18887 |