广义两分量Camassa-Holm方程的柯西问题

张颖, 张江红

数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 923-934.

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数学学报 ›› 2013, Vol. 56 ›› Issue (6) : 923-934. DOI: 10.12386/A2013sxxb0088
论文

广义两分量Camassa-Holm方程的柯西问题

    张颖1, 张江红2
作者信息 +

The Cauchy Problem for a Generalized Two-Component Camassa-Holm System

    Ying ZHANG1, Jiang Hong ZHANG2
Author information +
文章历史 +

摘要

研究了一个广义两分量Camassa-Holm方程的柯西问题,该模型可从经过线性切流的浅水波的理论机制中得出.文中讨论了该模型的爆破现象, 建立了爆破发生时柯西问题的初始值满足的充分条件. 同时研究了强解的持久和唯一连续性.

Abstract

We investigate a generalized two-component Camassa-Holm system which can be derived from the theory of shallow water waves moving over a linear shear flow. We study the blow-up phenomena and establish a sufficient condition on the initial data to guarantee wave-breaking for the system. Moreover, the persistence properties of the strong solutions are also analyzed.

关键词

广义Camassa-Holm方程 / 爆破 / 持久性 / 唯一连续性

Key words

generalized Camassa-Holm system / blow-up / persistence properties / strong solutions

引用本文

导出引用
张颖, 张江红. 广义两分量Camassa-Holm方程的柯西问题. 数学学报, 2013, 56(6): 923-934 https://doi.org/10.12386/A2013sxxb0088
Ying ZHANG, Jiang Hong ZHANG. The Cauchy Problem for a Generalized Two-Component Camassa-Holm System. Acta Mathematica Sinica, Chinese Series, 2013, 56(6): 923-934 https://doi.org/10.12386/A2013sxxb0088

参考文献

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基金

国家自然科学基金资助项目(11101332);数学天元基金资助项目(11226195)

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