Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation

We consider finite time blow up solutions to the critical nonlinear Schrödinger equation For a suitable class of initial data in the energy space H1, we prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of L2 mass at the blow up point, the second part corresponds to the regular part and has a strong L2 limit at blow up time.

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