The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation

We consider the critical nonlinear Schrdinger equation iu t = -u-|u| 4 N u with initial condition u(0, x) = u 0 in dimension N = 1. For u 0 H 1 , local existence in the time of solutions on an interval [0, T ) is known, and there exist finite time blow-up solutions, that is, u 0 such that lim tT 1.