A Sufficient Condition for Blowup of the Nonlinear Klein-Gordon Equation with Positive Initial Energy in FLRW Spacetimes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916270986756096 |
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| author | McCollum, Jonathon Mwamba, Gregory Oliver, Jesús |
| author_facet | McCollum, Jonathon Mwamba, Gregory Oliver, Jesús |
| contents | In this paper we demonstrate a sufficient condition for blowup of the nonlinear Klein-Gordon equation with arbitrarily positive initial energy in Friedmann-Lemaître-Robertson-Walker spacetimes. This is accomplished using an established concavity method that has been employed for similar PDEs in Minkowski space. This proof relies on the energy inequality associated with this equation, $E(t_0)\geq E(t)$, also proved herein using a geometric method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00950 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Sufficient Condition for Blowup of the Nonlinear Klein-Gordon Equation with Positive Initial Energy in FLRW Spacetimes McCollum, Jonathon Mwamba, Gregory Oliver, Jesús Analysis of PDEs General Relativity and Quantum Cosmology In this paper we demonstrate a sufficient condition for blowup of the nonlinear Klein-Gordon equation with arbitrarily positive initial energy in Friedmann-Lemaître-Robertson-Walker spacetimes. This is accomplished using an established concavity method that has been employed for similar PDEs in Minkowski space. This proof relies on the energy inequality associated with this equation, $E(t_0)\geq E(t)$, also proved herein using a geometric method. |
| title | A Sufficient Condition for Blowup of the Nonlinear Klein-Gordon Equation with Positive Initial Energy in FLRW Spacetimes |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2406.00950 |