Global Weak Solution for the Periodic 2-order Camassa-Holm Equation

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摘要:

考虑了二阶Camassa-Holm方程在周期条件下的柯西问题.利用奇异扰动的方法构造了二阶Camassa-Holm方程的黏性方程.通过压缩映射原理以及先验估计讨论了方程黏性解的存在性,然后根据黏性解的紧致性得到了周期的二阶Camassa-Holm方程在有限能量空间上弱整体解的存在性.

In this paper,the Cauchy problem of the second-order Camassa-Holm equation under periodic conditions is considered.With singular perturbation approach,a viscous equation is constructed.Applying contraction mapping principle and priori estimate,the existence of viscous solutions is obtained.Then,according to the compactness of viscous solutions,the existence of global weak solution for the periodic 2-order Camassa-Holm equation in finite energy space is obtained.

作者:

丁丹平章双华

机构地区:

江苏大学理学院

出处:

《betway官方app 学报：自然科学版》 CAS 北大核心 2015年第4期7-15,共9页

基金:

国家自然科学基金(11371175)

关键词:

周期的二阶Camassa-Holm方程弱解整体存在性

periodic 2-order Camassa-Holm equation weak solution global existence

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