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Schrödinger flow near harmonic maps

✍ Scribed by Stephen Gustafson; Kyungkeun Kang; Tai-Peng Tsai

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 294 KB
Volume: 60
Category: Article
ISSN: 0010-3640
DOI: 10.1002/cpa.20143

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✦ Synopsis

Abstract

For the Schrödinger flow from ℝ^2^ × ℝ^+^ to the 2‐sphere 𝕊^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.

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