Remarks on the blow-up rate for critical nonlinear Schrödinger equation with harmonic potential

摘要

We consider the blow-up solutions of the Cauchy problem for the critical nonlinear Schrödinger equation with a harmonic potential, which models the attractive Bose–Einstein condensate. We establish the sharp lower and upper bounds of blow-up rate as (blow-up time), which improve the result of [Q. Liu, Y. Zhou, J. Zhang, Upper and lower bound of the blow-up rate for nonlinear Schrödinger equation with a harmonic potential, Appl. Math. Comput. 172 (2006) 1121–1132].