Blow-up for the non linear Schrödinger equation in the “log log” regime

Nicolas Burq

Séminaire Bourbaki (2005-2006)

  • Volume: 48, page 33-54
  • ISSN: 0303-1179

Abstract

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In this talk we present some recent results by Merle and Raphael on analysis of blow-up solution for the L 2 critical non linear Schrödinger equation. In particular, we focus on their proof of the fact that initial data with negative energy (which had been known to blow up by the viriel identity) and with L 2 norm close to the ground states’s L 2 norm, do blow up in the “log log” regime and that this behaviour is stable.

How to cite

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Burq, Nicolas. "Explosion pour l’équation de Schrödinger au régime du “log log”." Séminaire Bourbaki 48 (2005-2006): 33-54. <http://eudml.org/doc/252167>.

@article{Burq2005-2006,
abstract = {On présente dans cet exposé des résultats récents de Merle et Raphael sur l’analyse des solutions explosives de l’équation de Schrödinger $L^2$ critique. On s’intéresse en particulier à leur preuve du fait que les solutions d’énergie négative (dont on savait qu’elles explosaient par l’argument du viriel) et dont la norme $L^2$ est proche de celle de l’état fondamental, explosent au régime du “log log”et que ce comportement est stable.},
author = {Burq, Nicolas},
journal = {Séminaire Bourbaki},
keywords = {non linear Schrödinger equations; blow-up},
language = {fre},
pages = {33-54},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Explosion pour l’équation de Schrödinger au régime du “log log”},
url = {http://eudml.org/doc/252167},
volume = {48},
year = {2005-2006},
}

TY - JOUR
AU - Burq, Nicolas
TI - Explosion pour l’équation de Schrödinger au régime du “log log”
JO - Séminaire Bourbaki
PY - 2005-2006
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 48
SP - 33
EP - 54
AB - On présente dans cet exposé des résultats récents de Merle et Raphael sur l’analyse des solutions explosives de l’équation de Schrödinger $L^2$ critique. On s’intéresse en particulier à leur preuve du fait que les solutions d’énergie négative (dont on savait qu’elles explosaient par l’argument du viriel) et dont la norme $L^2$ est proche de celle de l’état fondamental, explosent au régime du “log log”et que ce comportement est stable.
LA - fre
KW - non linear Schrödinger equations; blow-up
UR - http://eudml.org/doc/252167
ER -

References

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