Conformal scattering of the Maxwell-scalar field system on de Sitter space
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arXiv
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866909690558939136 |
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| author | Taujanskas, Grigalius |
| author_facet | Taujanskas, Grigalius |
| contents | We prove small data energy estimates of all orders of differentiability between past null infinity and future null infinity of de Sitter space for the conformally invariant Maxwell-scalar field system. This allows us to construct bounded and invertible, but nonlinear, scattering operators taking past asymptotic data to future asymptotic data. We also deduce exponential decay rates for solutions with data having at least two derivatives, and for more regular solutions discover an asymptotic decoupling of the scalar field from the charge. The construction involves a carefully chosen complete gauge fixing condition which allows us to control all components of the Maxwell potential, and a nonlinear Grönwall inequality for higher order estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1809_01559 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Conformal scattering of the Maxwell-scalar field system on de Sitter space Taujanskas, Grigalius Analysis of PDEs General Relativity and Quantum Cosmology 83C30, 35Q75, 83C50 We prove small data energy estimates of all orders of differentiability between past null infinity and future null infinity of de Sitter space for the conformally invariant Maxwell-scalar field system. This allows us to construct bounded and invertible, but nonlinear, scattering operators taking past asymptotic data to future asymptotic data. We also deduce exponential decay rates for solutions with data having at least two derivatives, and for more regular solutions discover an asymptotic decoupling of the scalar field from the charge. The construction involves a carefully chosen complete gauge fixing condition which allows us to control all components of the Maxwell potential, and a nonlinear Grönwall inequality for higher order estimates. |
| title | Conformal scattering of the Maxwell-scalar field system on de Sitter space |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology 83C30, 35Q75, 83C50 |
| url | https://arxiv.org/abs/1809.01559 |