题目：On the Cauchy Problem for the (modified) Two-component Euler-Poincare Equations

报告人: 向昭银   电子科技大学

时  间: 5月12日 星期一 下午4:00 -5:30

地  点: 管理科研楼1611会议室

摘 要:  In this talk, we first use the classical energy methods to establish the local existence of unique classical solutions as well as two blow-up criteria for the Cauchy problem of the two-component Euler-Poincare equations. Then by using the particle trajectory and the Littlewood-Paley decomposition theory, we show that for a large of smooth initial data with some concentration property, the corresponding solutions will blow up in finite time. In the case of one component, we also obtain the precise blow-up rate estimates and global existence for the initial data with some non-positive property at the original. Next, we investigate the zero density limit and the zero dispersion limit. At the end of the talk, we also briefly demonstrate a Liouville type theorem for the stationary weak solutions. This is a joint work with Dr. Renjun Duan.

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