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

2025/01/30 by J. Arturo Olvera-Santamaría, Olvera-Santamaria, J. Arturo
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2501.18133

openalex publication_date 2025/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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