论文标题
关于阳米尔斯 - 吉格斯和lorenz仪表中的杨米尔斯 - 迪拉克系统的缩放临界规律性
On the scaling critical regularity of the Yang-Mills-Higgs and the Yang-Mills-Dirac system in the Lorenz gauge
论文作者
论文摘要
在本文中，我们研究了Lorenz Gauge中$（1+3）$ - 尺寸Yang-Mills-higgs（YMH）和Yang-Mills-Dirac（YMD）系统的本地良好性。由于（YMH）中有一些双线性项，这是缺乏无效结构的，因此最多可以在能量空间中获得良好的性能。但是，我们通过在角变量中施加额外的加权规律性来达到（YMH）的临界规律性。在（YMD）中，要使耦合系统持续存在，需要将角度规则施加到狄拉克纺纱器上，并与Yang-Mills量规势和曲率一样多。然后，我们可以使用角度规律性而不是纺纱场的无效结构来证明（YMD）的临界规律性。通过这种方式，我们提出了一种同时攻击（YMH）和（YMD）的临界规律性的方法。该结果是我们最近在lorenz量规\ cite {hong}中对杨米尔斯系统的研究的应用。
In this paper, we study the local well-posedness of the $(1+3)$-dimensional Yang-Mills-Higgs (YMH) and the Yang-Mills-Dirac (YMD) system in the Lorenz gauge. Since there is some bilinear term in (YMH), which is a lack of null structure, one may obtain the well-posedness at most the energy space. However, we attain the scaling critical regularity of (YMH) by imposing the extra weighted regularity in the angular variables. In (YMD), for the coupled system to persist in time, it is required to impose the angular regularity on the Dirac spinor as much as the Yang-Mills gauge potential and curvature. We can then prove the scaling critical regularity of (YMD) using angular regularity instead of the null structure of the spinor field. In this manner, we present an approach to attack the scaling critical regularity of (YMH) and (YMD) simultaneously. This result is an application of our recent study on the Yang-Mills system in the Lorenz gauge \cite{hong}.
