论文标题
全球解决3D Dirac-具有均匀能量边界的Klein-Gordon系统
Global solution to the 3D Dirac--Klein-Gordon system with uniform energy bounds
论文作者
论文摘要
在（1+3）尺寸的Minkowski时空，对于小的常规初始数据，众所周知，Dirac-Klein-Gordon系统允许全局解决方案。在本文中，我们旨在建立该系统解决方案总能量的统一界限。证明依赖于Klainerman的矢量场和Alinhac的幽灵重量方法。 主要困难源于三个空间维度在狄拉克和波浪成分的缓慢衰减性质。为了克服困难，需要对该系统的结构有深刻的理解，以及需要进行新的加权保形能量估计。此外，我们还为系统提供了一些散射结果。
On the (1+3) dimensional Minkowski spacetime, for small, regular initial data, it is well-known that the Dirac-Klein-Gordon system admits a global solution. In the present paper, we aim to establish the uniform boundedness of the total energy of the solution for this system. The proof relies on Klainerman's vector field and Alinhac's ghost weight methods. The main difficulty originates from the slow decay nature of the Dirac and wave components in three space dimensions. To overcome the difficulty, a sharp understanding of the structure for this system, and a new weighted conformal energy estimate are required. In addition, we also provide a few scattering results for the system.
