Curvature Blow-up for the Higher-order Camassa-Holm Equations
Curvature Blow-up for the Higher-order Camassa-Holm Equations
复制标题
高阶 Camassa-Holm 方程的曲率放大
DOI：
10.1007/s10884-019-09793-8
复制
发表时间：
2020
影响因子：
1.3
通讯作者：
Ying Fu
中科院分区：
文献类型：
--
作者：
Changzheng Qu;Ying Fu
本文致力于了解高阶非线性如何影响色散动力学。作为原型，研究了一类高阶 Camassa-Holm 方程，它可以被视为 Camassa-Holm 方程的推广。柯西问题在Besov 空间和Sobolev 空间中的局部适定性成立。此外，还采用精细分析来研究奇点的形成，并提供了导致解的二阶导数有限时间爆炸的初始数据的一些充分条件。
This paper is devoted to understanding how higher-order nonlinearities affect the dispersive dynamics. As a prototype, a class of higher-order Camassa–Holm equations which can be viewed as a generalization of the Camassa–Holm equation is studied. The local well-posedness of the Cauchy problem in Besov spaces and Sobolev spaces is established. Furthermore, a delicate analysis is employed to investigate the formation of singularities, and some sufficient conditions on initial data that lead to the finite time blow-up of the second-order derivative of the solutions are provided.