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

• 成果类型: Article
• 署名作者: Merle, Frank; Raphael, Pierre; Rodnianski, Igor
• 署名单位: CY Cergy Paris Universite; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0427-y
• 发表日期: 2013
• 页码: 249-365
• 关键词: harmonic maps; up rate; SINGULARITIES; STABILITY; EVOLUTION; SPACE; mass

摘要

We consider the energy critical Schrodinger 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.