报告题目：Dynamics of the energy critical nonlinear Schrödinger equation with inverse square potential

报告时间：2017年9月29日上午10：00 - 12：00（星期五）

报告地点：理科楼321

报告人：杨凯 香港科技大学 博士后

Abstract

  We consider the Cauchy problem for the focusing energy critical nonlinear Schrödinger equation with inverse square potential in the radial case. We prove that among all solutions with the same energy as the ground state solution W, there are only two (up to symmetries) solutions W+，W- that are exponential close to W and serve as the threshold of scattering and blow-up. All solutions with the same energy will blow up both forward and backward in time if they go beyond the upper threshold W+; all solutions with the same energy will scatter both forward and backward in time if they fall below the lower threshold W-.