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Schrödinger flow near harmonic maps
Author(s) -
Gustafson Stephen,
Kang Kyungkeun,
Tsai TaiPeng
Publication year - 2007
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20143
Subject(s) - equivariant map , harmonic map , mathematics , harmonic , flow (mathematics) , energy (signal processing) , schrödinger's cat , mathematical analysis , scale (ratio) , geometry , pure mathematics , physics , quantum mechanics , statistics
For the Schrödinger flow from ℝ 2 × ℝ + to the 2‐sphere 2 , it is not known if finite energy solutions can blow up in finite time. We study equivariant solutions whose energy is near the energy of the family of equivariant harmonic maps. We prove that such solutions remain close to the harmonic maps until the blowup time (if any), and that they blow up if and only if the length scale of the nearest harmonic map goes to 0. © 2006 Wiley Periodicals, Inc.