Scattering results for the (1+4) dimensional massive Maxwell-Dirac system under Lorenz gauge condition
This paper investigates the \emph{massive} Maxwell-Dirac system under the Lorenz gauge condition in (4+1) dimensional Minkowski space. The focus is on establishing global existence and scattering results for small solutions on the weighted Sobolev class. The imposition of the Lorenz gauge condition...
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| Main Author: | |
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| Format: | Journal Article |
| Language: | English |
| Published: |
21-12-2023
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | This paper investigates the \emph{massive} Maxwell-Dirac system under the
Lorenz gauge condition in (4+1) dimensional Minkowski space. The focus is on
establishing global existence and scattering results for small solutions on the
weighted Sobolev class. The imposition of the Lorenz gauge condition transforms
the Maxwell-Dirac system into a set of Dirac equations coupled with an
electromagnetic potential derived from five quadratic wave equations. To
achieve a comprehensive understanding of the global solution and its behavior,
we employ various energy estimates based on the space-time resonance argument.
This involves addressing diverse resonance functions arising from the free
Dirac and wave propagators. Additionally, we identify the space-time resonant
sets associated with the \emph{massive} Maxwell-Dirac system. |
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| DOI: | 10.48550/arxiv.2312.13621 |