论文标题
通用Camassa-Holm系统的本地和全球分析性
Local and global analyticity for a generalized Camassa-Holm system
论文作者
论文摘要
我们解决了R. M. Chen和Y. Liu引入的广义两组分子CAMASSA-HOLM系统的分析性Cauchy问题。我们在某些条件下显示了独特的本地/全球分析解决方案的存在。这是针对类似Camassa-Holm的系统的全球分析性的第一个结果。证明方法基本上是由Barostichi，Himonas和Petronilho开发的。他们的证明和我们的主要差异是双重的：（i）陈和刘的系统在两个未知数中并不符合，我们的估计并不是对文章中的陈述的微不足道的概括，（ii）我们通过使用较少的功能空间来简化他们的论点，并且主要结果以简单和自然的方式表示。
We solve the analytic Cauchy problem for the generalized two-component Camassa-Holm system introduced by R. M. Chen and Y. Liu. We show the existence of a unique local/global-in-time analytic solution under certain conditions. This is the first result about global analyticity for a Camassa-Holm-like system. The method of proof is basically that developed by Barostichi, Himonas and Petronilho. The main differences of their proof and ours are twofold: (i) the system of Chen and Liu is not symmetic in the two unknowns and our estimates are not trivial generalization of those in their articles, (ii) we have simplified their argument by using fewer function spaces and the main result is stated in a simple and natural way.
