Scattering for the Equivariant U(1) Problem
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909416152891392 |
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| author | Gudapati, Nishanth |
| author_facet | Gudapati, Nishanth |
| contents | Extending our previous works on the Cauchy problem for the $2+1$ equivariant Einstein-wave map system, we prove that the linear part dominates the nonlinear part of the wave maps equation coupled to the full set of the Einstein equations, for small data. A key ingredient in the proof is a nonlinear Morawetz estimate for the fully coupled equivariant Einstein-wave maps. The $2+1$ dimensional Einstein-wave map system occurs naturally in the U(1) symmetric $3+1$ dimensional vacuum Einstein equations of general relativity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_01157 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Scattering for the Equivariant U(1) Problem Gudapati, Nishanth General Relativity and Quantum Cosmology Analysis of PDEs 83C05, 35L51 Extending our previous works on the Cauchy problem for the $2+1$ equivariant Einstein-wave map system, we prove that the linear part dominates the nonlinear part of the wave maps equation coupled to the full set of the Einstein equations, for small data. A key ingredient in the proof is a nonlinear Morawetz estimate for the fully coupled equivariant Einstein-wave maps. The $2+1$ dimensional Einstein-wave map system occurs naturally in the U(1) symmetric $3+1$ dimensional vacuum Einstein equations of general relativity. |
| title | Scattering for the Equivariant U(1) Problem |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs 83C05, 35L51 |
| url | https://arxiv.org/abs/2204.01157 |