Đề tài "The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr¨odinger equation "

The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr¨dinger equation o By Frank Merle and Pierre Raphael Abstract We consider the critical nonlinear Schr¨dinger equation iut = −∆u−|u| N u o with initial condition u(0, x) = u0 in dimension N = 1. For u0 ∈ 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, u0 such that limt↑