论文标题
关于3D Klein-Gordon-Zakharov系统的全球适应性和散射
On the global well-posedness and scattering of the 3D Klein-Gordon-Zakharov system
论文作者
论文摘要
在本文中，我们对3D Klein-Gordon-Zakharov方程的全球适应性感兴趣，并具有较小的初始数据。我们显示了对全局解决方案的能量的统一界限，而无需对初始数据进行任何紧凑的假设。我们证明的主要新颖性是应用修改后的Alinhac的幽灵重量方法以及新开发的正常形式估计值，以弥补缺乏时空扩展矢量场的缺乏；此外，我们清楚地描述了初始数据的较小条件。
In this paper we are interested in the global well-posedness of the 3D Klein-Gordon-Zakharov equations with small initial data. We show the uniform boundedness of the energy for the global solution without any compactness assumptions on the initial data. The main novelty of our proof is to apply a modified Alinhac's ghost weight method together with a newly developed normal-form type estimate to remedy the lack of the space-time scaling vector field; moreover, we give a clear description of the smallness conditions on the initial data.
