Global solution to the Klein-Gordon-Zakharov equations with uniform energy bounds

2021/01/08 by Shijie Dong, Dong, Shijie
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2101.02927

Abstract

We are interested in the Klein-Gordon-Zakharov equations in ℝ¹⁺³, and we aim to show that the energy for the global solution to the equations is uniformly bounded, and we do not require the compactness assumption on the initial data. To achieve these goals, the key is to apply Alinhac's ghost weight energy estimates adapted to the Klein-Gordon equations.

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