Dynamique explosive de solutions régulières équivariantes de l'application de Schrödinger énergie critique

Translated title of the contribution: Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map

Frank Merle, Pierre Raphaël, Igor Rodnianski

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

We consider the energy critical Schrödinger map ∂tu=u∧δu to the 2-sphere for equivariant initial data of homotopy number k=1. We show the existence of a set of smooth initial data arbitrarily close to the ground state harmonic map Q1 in the scale invariant norm Ḣ1 which generate finite time blow up solutions. We give in addition a sharp description of the corresponding singularity formation which occurs by concentration of a universal bubble of energy. where θ*∈R, u*∈Ḣ1, R is a rotation and the concentration rate is given for some κ(u)>0 by.

Translated title of the contributionBlow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map
Original languageFrench
Pages (from-to)279-283
Number of pages5
JournalComptes Rendus Mathematique
Volume349
Issue number5-6
DOIs
StatePublished - Mar 1 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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