2023/11/30 by Xinyu Cheng, Cheng, Xinyu · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2312.00821
openalex publication_date 2023/11/30 · openalex created_date 2023/12/06 · openalex updated_date 2026/07/28
In this paper we are interested in the coupled wave and Klein-Gordon equations in ℝ+×ℝ2. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the global solution without any compactness assumptions on the initial data. In addition, we also demonstrate the pointwise asymptotic behavior of the solution pair. In order to achieve that we apply a modified Alinhac's ghost weight method together with a newly developed normal-form framework to remedy the lack of the space-time scaling vector field. Finally we show the global solutions scatter linearly strongly for the Klein-Gordon field ϕ and weakly for the wave field n as t→+∞. To our best knowledge such scattering phenomenon is novel in the literature.