Lipschitz metric for the periodic second-order Camassa Holm equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:451

Article

Ding, Danping¹  Zhang, Shuanghua¹ 

[1] Jiangsu Univ, Dept Math, Zhenjiang 212013, Jiangsu, Peoples R China

关键词: Camassa-Holm equation;    Continuous semigroup;    Lipschitz metric;    Local weak solution;    Periodic second-order;    Relabeling;   

DOI  :  10.1016/j.jmaa.2017.02.018

来源: Elsevier

【 摘 要 】

In this study, we consider the Cauchy problem for the second-order Camassa- Holm equation with periodic initial data uo. Using the vanishing viscosity method, the local weak solution of the equation is obtained in the finite energy space. A continuous semigroup of weak conservative solutions in Lagrangian coordinates is constructed. In particular, for any two solutions u(t) and v(t) of the equation, a Lipschitz metric dD is constructed with the property that d(D), (u(t), v(t)) <= e(Ct)d(D)(u(0), v(0)). (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free