Academic Report
Title: Global well-posedness and blow-up phenomenon for a generalization two component Camassa-Holm system
Reporter: HUANG Jingchi (School of mathematics, Zhongshan University)
Time: July16, 2018 (Monday) PM 14:00-15:00
Location:A1101# room, Innovation Park Building
Contact: YU Fang (tel:84708351-8025)
Abstract: A new generalized two component Camassa-Holm system is derived via the energy variational approach. This system has two parameter which depend on the energy functional. The initial value problem is investigated. The local well-posedness is obtained when the initial density is away from vacuum. Taking advantage of the method of characteristics and the conservation laws we prove a blow up criteria. According to the blow up criteria, we can prove the finite time blow up result under some suitable condition. Moreover, we give some exact expression of traveling solutions. This is a joint work with Yuhui Chen, Wei Luo and Fang Yu.
The brief introduction to the reporter: Huang Jingchi received his doctorate in Institute of mathematics of the Chinese Academy of Sciences in 2013 and worked in postdoctoral research in Pennsylvania State University from 2013 to 2015. He is now working at the school of mathematics at Zhongshan University and the main research area is partial differential equations in fluid mechanics At present. He has won the special prize of the Dean scholarship of the Chinese Academy of Sciences. He has published 7 papers in the famous international magazine such as Arch. Ration. Mech. Anal., J. Funct. Anal. and J. Math. Pures Appl.and he has been supported by the National Natural Science Foundation of China Youth Foundation.
