广义交叉耦合Camassa-Holm方程解的Gevrey正则性和解析性

Gevrey Regularity and Analyticity for a Generalized Cross-coupled Camassa-Holm System

本文主要研究具有高阶非线性的广义交叉耦合Camassa-Holm方程的柯西问题.首先通过构造一个新的Banach空间得到了推广的Ovsyannikov定理;然后应用该定理和Sobolev-Gevrey空间的基本性质,得到了广义交叉耦合Camassa-Holm方程解的Gevrey正则性和解析性;最后获得了广义交叉耦合Camassa-Holm方程解的存在时间的下界.

This paper mainly focuses on the Cauchy problem for a generalized cross-coupled Camassa-Holm system with higher-order nonlinearities.The generalized Ovsanynikov theorem is obtained by constructing a new Banach space,and then the Gevrey regularity and analyticity of the data-to-solution map of the generalized cross-coupled Camassa-Holm system are obtained by using the theorem and the basic properties of Sobolev-Gevrey spaces.In addition,a lower bound of the lifespan of the solution map is also obtained.