Article

Communications in Mathematical Physics

, Volume 253, Issue 3, pp 675-704

First online:

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

  • Frank MerleAffiliated withDépartment de Mathématiques, Université de Cergy–PontoiseInstitute for Advanced StudyCNRS
  • , Pierre RaphaelAffiliated withDépartment de Mathématiques, Université de Cergy–PontoiseInstitute for Advanced Study

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Abstract

We consider finite time blow up solutions to the critical nonlinear Schrödinger equation https://static-content.springer.com/image/art%3A10.1007%2Fs00220-004-1198-0/MediaObjects/s00220-004-1198-0flb1.gif 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.