The Null Condition and Global Existence for Nonlinear Wave Equations on\n Slowly Rotating Kerr Spacetimes

2010/09/21 by Jonathan Luk, Luk, Jonathan
Physics and Astronomy · #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1009.4109

openalex publication_date 2010/09/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We study a semilinear equation with derivatives satisfying a null condition\non slowly rotating Kerr spacetimes. We prove that given sufficiently small\ninitial data, the solution exists globally in time and decays with a\nquantitative rate to the trivial solution. The proof uses the robust vector\nfield method. It makes use of the decay properties of the linear wave equation\non Kerr spacetime, in particular the improved decay rates in the region\n r\≤ \(t)/(4) .\n

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