, Volume 253, Issue 3, pp 675-704
Date: 20 Oct 2004

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

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Abstract

We consider finite time blow up solutions to the critical nonlinear Schrödinger equation For a suitable class of initial data in the energy space H 1, we prove that the solution splits in two parts: the first part corresponds to the singular part and accumulates a quantized amount of L 2 mass at the blow up point, the second part corresponds to the regular part and has a strong L 2 limit at blow up time.

Communicated by P. Constantin
Part of this work has been supported by grant DMS-0111298.