The Maxwell-Klein-Gordon equation with scattering data
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913770747461632 |
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| author | Dai, Wei Mei, He Wei, Dongyi Yang, Shiwu |
| author_facet | Dai, Wei Mei, He Wei, Dongyi Yang, Shiwu |
| contents | It has been shown in [Yang-Yu 2019] that general large solutions to the Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space $\mathbb{R}^{1+3}$ decay like linear solutions. One hence can define the associated radiation field on the future null infinity as the limit of $(r\underlineα, rϕ)$ along the out going null geodesics. In this paper, we show the existence of a global solution to the MKG system which scatters to any given sufficiently localized radiation field with arbitrarily large size and total charge. The result follows by studying the characteristic initial value problem for the MKG system with general large data by using gauge invariant vector field method. We in particular extend the small data result of He in \cite{MR4299134} to a class of general large data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08732 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Maxwell-Klein-Gordon equation with scattering data Dai, Wei Mei, He Wei, Dongyi Yang, Shiwu Analysis of PDEs 35L05, 35Q61, 35Q70 It has been shown in [Yang-Yu 2019] that general large solutions to the Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space $\mathbb{R}^{1+3}$ decay like linear solutions. One hence can define the associated radiation field on the future null infinity as the limit of $(r\underlineα, rϕ)$ along the out going null geodesics. In this paper, we show the existence of a global solution to the MKG system which scatters to any given sufficiently localized radiation field with arbitrarily large size and total charge. The result follows by studying the characteristic initial value problem for the MKG system with general large data by using gauge invariant vector field method. We in particular extend the small data result of He in \cite{MR4299134} to a class of general large data. |
| title | The Maxwell-Klein-Gordon equation with scattering data |
| topic | Analysis of PDEs 35L05, 35Q61, 35Q70 |
| url | https://arxiv.org/abs/2302.08732 |