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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2501.18133 |
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| _version_ | 1866909470052843520 |
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| author | Olvera-Santamaria, J. Arturo |
| author_facet | Olvera-Santamaria, J. Arturo |
| contents | In this paper, we establish the global existence of a semi-linear class of hyperbolic equations in 3+1 dimensions, that satisfy the bounded weak null condition. We propose a conformal compactification of the future directed null-cone in Minkowski spacetime, enabling us to establish the solution to the wave equation in a neighbourhood of future null infinity. Using this framework, we formulate a conformal symmetric hyperbolic Fuchsian system of equations. The existence of solutions to this Fuchsian system follows from an application of the existence theory developed in [1], and [2]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global existence for semi-linear hyperbolic equations in a neighbourhood of future null infinity Olvera-Santamaria, J. Arturo Analysis of PDEs In this paper, we establish the global existence of a semi-linear class of hyperbolic equations in 3+1 dimensions, that satisfy the bounded weak null condition. We propose a conformal compactification of the future directed null-cone in Minkowski spacetime, enabling us to establish the solution to the wave equation in a neighbourhood of future null infinity. Using this framework, we formulate a conformal symmetric hyperbolic Fuchsian system of equations. The existence of solutions to this Fuchsian system follows from an application of the existence theory developed in [1], and [2]. |
| title | Global existence for semi-linear hyperbolic equations in a neighbourhood of future null infinity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.18133 |