论文标题
2D Dirac-Klein-Gordon方程的小型数据解决方案的全球行为
Global Behavior of Small Data Solutions for The 2D Dirac-Klein-Gordon Equations
论文作者
论文摘要
在本文中，我们对二维Dirac-Klein-Gordon系统感兴趣，该系统是粒子物理学中的基本模型。在大规模的标量场和无质量的迪拉克场的情况下，我们研究了该系统的小数据解决方案的全球行为。更确切地说，我们的主要结果是双重的：1）对于溶液的点估计，我们显示出明显的时间衰减，这意味着该系统的渐近稳定性； 2）我们显示该系统的线性散射结果，这是一个基本问题，当它被视为分散方程。我们的结果对于一般的小型初始数据有效，尤其是对初始数据的支持没有限制。
In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field and a massless Dirac field. More precisely, our main result is twofold: 1) we show sharp time decay for the pointwise estimates of the solutions which imply the asymptotic stability of this system; 2) we show the linear scattering result of this system which is a fundamental problem when it is viewed as dispersive equations. Our result is valid for general small, high-regular initial data, in particular, there is no restriction on the support of the initial data.
