论文标题
洛伦兹仪表中的全球良好及格和能量关键的麦克斯韦 - 克莱因 - 戈登系统的散射
Global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon system in the Lorenz gauge
论文作者
论文摘要
我们研究$（1+4）$ - lorenz仪表中的$（1+4）$ - 麦克斯韦 - 克莱恩 - 戈登系统（MKG）。由于Lorenz仪表中的（MKG）没有明显的空结构，因此处理非线性并不容易。为了克服这一障碍，我们施加了额外的角度规律性。在本文中，我们证明了在比例不变空间中的小数据的全球体积和（MKG）的散射，该空间在角变量中具有额外的加权规律性。我们的主要改进是实现限制规律性指数，并证明洛伦兹仪表中（MKG）的全球解决方案存在。
We study initial value problem of the $(1+4)$-dimensional Maxwell-Klein-Gordon system (MKG) in the Lorenz gauge. Since (MKG) in the Lorenz gauge does not possess an obvious null structure, it is not easy to handle the nonlinearity. To overcome this obstacle, we impose an additional angular regularity. In this paper, we prove global well-posedness and scattering of (MKG) for small data in a scale-invariant space which has extra weighted regularity in the angular variables. Our main improvement is to attain the scaling critical regularity exponent and prove global existence of solutions to (MKG) in the Lorenz gauge.
