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

Abstract

We consider the critical nonlinear Schrödinger equation iut = -Δu - |u|4/N u with initial condition u(0, x) = u 0 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 lim t↑ 1.