一个高阶μ-Camassa-Holm方程Cauchy问题解的解析性

Analyticity of the solutions of the Cauchy problem associated with aμ-Camassa-Holm equation with higher-order nonlinearity

该文通过构造一族递减的Banach空间,利用抽象的Cauchy-Kowalevski定理研究了一个高阶μ-Camassa-Holm方程Cauchy问题解的解析性.所得到的结论可直接应用到μ-Camassa-Holm方程和Hunter-Saxton方程上.

By constructing a scale of decreasing Banach spaces and using the abstact Cauchy-Kowalevski theorem,analyticity of the solutions to Cauchy problem associated with aμ-Camassa-Holm equation with high-order nonlinearity is studied in this paper.The results can be directly applied toμ-Camassa-Holm equation and Hunter-Saxton equation.