Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem

Frank Merle, Pierre Raphaël, Igor Rodnianski

Research output: Contribution to journalArticle

52 Scopus citations

Abstract

We consider the energy critical Schrödinger map problem with the 2-sphere target for equivariant initial data of homotopy index k=1. We show the existence of a codimension one set of smooth well localized initial data arbitrarily close to the ground state harmonic map in the energy critical norm, which generates finite time blowup solutions. We give a sharp description of the corresponding singularity formation which occurs by concentration of a universal bubble of energy.

Original languageEnglish (US)
Pages (from-to)249-365
Number of pages117
JournalInventiones Mathematicae
Volume193
Issue number2
DOIs
StatePublished - Aug 1 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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