Large data decay of Yang-Mills-Higgs fields on Minkowski and de Sitter spacetimes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866916723767115776 |
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| author | Taujanskas, Grigalius |
| author_facet | Taujanskas, Grigalius |
| contents | We extend Eardley and Moncrief's $L^\infty$ estimates for the conformally invariant Yang-Mills-Higgs equations to the Einstein cylinder. Our method is to first work on Minkowski space and localise their estimates, and then carry them to the Einstein cylinder by a conformal transformation. By patching local estimates together, we deduce global $L^\infty$ estimates on the cylinder, and extend Choquet-Bruhat and Christodoulou's small data well-posedness result to large data. Finally, by employing another conformal transformation, we deduce exponential decay rates for Yang-Mills-Higgs fields on de Sitter space, and inverse polynomial decay rates on Minkowski space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_08519 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Large data decay of Yang-Mills-Higgs fields on Minkowski and de Sitter spacetimes Taujanskas, Grigalius Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry We extend Eardley and Moncrief's $L^\infty$ estimates for the conformally invariant Yang-Mills-Higgs equations to the Einstein cylinder. Our method is to first work on Minkowski space and localise their estimates, and then carry them to the Einstein cylinder by a conformal transformation. By patching local estimates together, we deduce global $L^\infty$ estimates on the cylinder, and extend Choquet-Bruhat and Christodoulou's small data well-posedness result to large data. Finally, by employing another conformal transformation, we deduce exponential decay rates for Yang-Mills-Higgs fields on de Sitter space, and inverse polynomial decay rates on Minkowski space. |
| title | Large data decay of Yang-Mills-Higgs fields on Minkowski and de Sitter spacetimes |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/1902.08519 |