本项目主要研究四个分支的Camass-Holm型系统的弱解问题, 它是Camassa-Holm方程, Degasperis-Procesi方程, Novikov方程等方程的推广。 从这个系统的整体强解出发, 我们得到一系列近似解; 结合补偿列紧方法和Yang测度理论我们最终得到这个系统Cauchy问题弱解的存在性。

In this project, we consider a four-component Camassa-Holm type system, which is considered as a generalization of Camassa-Holm equation, Degasperis-Procesi equation, Novikov equation and other equations. Based on the existence of global strong solutions to this system, we get a sequence of approximate solutions; by using the compensated compactness method and the Yong measure theory, we finally obtain global weak solutions to the Cauchy problem of this system.