A conformal-type energy inequality on hyperboloids and its application to quasi-linear wave equation in ℝ³⁺¹

2017/11/01 by Yue Ma, Hongjing Huang, Ma, Yue +1 · 1 citation
Engineering · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.00498

openalex publication_date 2017/11/01 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28

Abstract

In the present work, we will develop a conformal inequality in the hyperbolic foliation context which is analogous to the conformal inequality in the classical time-constant foliation context. Then as an application, we will apply this a priori estimate to the problem of global existence of quasi-linear wave equations in three spatial dimensions under null condition. With the aid of this inequality, we can establish more precise decay estimates on the global solution.

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• Stability of a wave and Klein-Gordon system with mixed coupling

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