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arXiv · 2501.18133

Global existence for semi-linear hyperbolic equations in a neighbourhood of future null infinity

J. Arturo Olvera-Santamaria
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Abstract

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].

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J. Arturo Olvera-Santamaria. 2025-01-30. Global existence for semi-linear hyperbolic equations in a neighbourhood of future null infinity. https://arxiv.org/abs/2501.18133

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