Communications in Mathematical Physics

, Volume 253, Issue 3, pp 675–704 | Cite as

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

  • Frank Merle
  • Pierre Raphael
Article

Abstract

We consider finite time blow up solutions to the critical nonlinear Schrödinger equation Open image in new window 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Frank Merle
    • 1
    • 2
    • 3
  • Pierre Raphael
    • 1
    • 2
  1. 1.Départment de MathématiquesUniversité de Cergy–PontoiseCergy-PontoiseFrance
  2. 2.Institute for Advanced StudyPrincetonUSA
  3. 3.CNRS 

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