论文标题
1+1维主手性模型中的全球存在和长时间行为，并应用于孤子的应用
Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons
论文作者
论文摘要
在本文中，我们将1+1维矢量的主手性手性场模型（PCF）视为简化贝林斯基 - 扎克哈罗夫对称性下真空爱因斯坦场方程。 PCF是一个可集成的模型，但是对其演变的严格描述远非完整。在这里，我们在适当选择的能源空间中提供了局部溶液的存在，以及在某些非退化条件下的小型全球平滑解决方案。我们还构建了病毒功能，从而清楚地描述了光锥体内部平滑全局溶液的衰减。最后，在PCF唯一的情况下提出了一些应用，这是迈向研究其非线性稳定性的第一步。
In this paper, we consider the 1+1 dimensional vector valued Principal Chiral Field model (PCF) obtained as a simplification of the Vacuum Einstein Field equations under the Belinski-Zakharov symmetry. PCF is an integrable model, but a rigorous description of its evolution is far from complete. Here we provide the existence of local solutions in a suitable chosen energy space, as well as small global smooth solutions under a certain non degeneracy condition. We also construct virial functionals which provide a clear description of decay of smooth global solutions inside the light cone. Finally, some applications are presented in the case of PCF solitons, a first step towards the study of its nonlinear stability.
