Explosion pour l'équation de Schrödinger au régime du

Explosion pour l'équation de Schrödinger au régime du « log log »

Burq, Nicolas

Séminaire Bourbaki : volume 2005/2006, exposés 952-966, Astérisque, no. 311 (2007), Exposé no. 953, pp. 33-54.

Résumé
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.

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.

EuDML Zbl | 1 citation dans Numdam

Classification : 35B30, 35B35, 35B65
Mot clés : equations de Schrödinger non linéaires, explosion
Keywords: non linear Schrödinger equations, blow-up

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     title = {Explosion pour l'\'equation de {Schr\"odinger} au r\'egime du {\guillemotleft} log log {\guillemotright}},
     booktitle = {S\'eminaire Bourbaki : volume 2005/2006, expos\'es 952-966},
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Burq, Nicolas. Explosion pour l'équation de Schrödinger au régime du « log log », dans Séminaire Bourbaki : volume 2005/2006, exposés 952-966, Astérisque, no. 311 (2007), Exposé no. 953, pp. 33-54. http://www.numdam.org/item/SB_2005-2006__48__33_0/

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