In this paper, we investigate the generalized Camassa–Holm equation with k + 1 degree nonlinearities. The global existence is established, provided that 0 < b < k and the initial data $y_0=(1-{\partial }_x^2)u_0$ do not change sign. Long time behavior for the support of momentum density is obtained, and more precisely, we deduce the limit of the support of momentum density as t goes to +∞.

中文翻译：

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具有 k+1 度非线性的广义 Camassa-Holm 方程的全局存在性和长时间行为

在本文中，我们研究了具有k + 1 度非线性的广义 Camassa-Holm 方程。全局存在成立，前提是 0 < b < k且初始数据${是}_0=(1-{\partial }_X^2){你}_0$请勿更改标志。获得了动量密度支持的长时间行为，更准确地说，我们推导出了当t趋于+∞ 时动量密度支持的极限。