Sharp upper and lower bounds on the blow-up rate for nonlinear Schrödinger equation with potential

摘要

We consider the blow-up solutions of the Cauchy problem for critical nonlinear Schrödinger equation with a repulsive harmonic potential. In terms of Merle and Raphaël’s recent arguments as well as Carles’ transform, the sharp upper and lower bounds of the blow-up rate are obtained.