Global Existence for Coupled 3-D Nonlinear Wave and Klein-Gordon Equations with Large Derivatives of Initial Data

2025/11/19 by Shang, Guocong
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.2511.15234

openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem of coupled 3-D wave and Klein-Gordon equations with a quadratic form of nonlinearity. We show global existence under several conditions, including large derivative data for wave equations and the null conditions.

Citations

• A non-linear damping structure and global stability of wave-Klein-Gordon coupled system in ℝ³⁺¹
• Cubic Dirac equations with a class of large data
• Strichartz estimates for the half wave/Klein-Gordon and Dirac Equations on compact manifolds without boundary
• The Maxwell-Klein-Gordon equation with scattering data
• Asymptotic behavior of 2D Wave-Klein-Gordon coupled system under null condition
• Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: A prototype of strong coupling case
• Global solution to the wave and Klein-Gordon system under null condition in dimension two
• Spectral stability of bi-frequency solitary waves in Soler and Dirac--Klein--Gordon models
• The null condition for quasilinear wave equations in two space dimensions I
• Normal forms and quadratic nonlinear Klein‐Gordon equations

Related

• Global solution to the wave and Klein-Gordon system under null condition in dimension two
• Stability of a coupled wave-Klein-Gordon system with non-compactly supported initial data
• Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities
• Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: weak coupling case
• Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: A prototype of strong coupling case