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

We consider the critical nonlinear Schr?odinger equation iut = -.u-|u| 4 N u with initial condition u(0, x) = u0 in dimension N = 1. For u0 . H1, local existence in the time of solutions on an interval [0, T) is known, and there exist finite time blow-up solutions, that is, u0 such that limt.T 1.

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