Schrödinger flow near harmonic maps

  1. Stephen Gustafson1,
  2. Kyungkeun Kang2,
  3. Tai-Peng Tsai1

Article first published online: 7 JUN 2006

DOI: 10.1002/cpa.20143

Issue

Communications on Pure and Applied Mathematics

Communications on Pure and Applied Mathematics

Volume 60, Issue 4, pages 463–499, April 2007

Additional Information

How to Cite

Gustafson, S., Kang, K. and Tsai, T.-P. (2007), Schrödinger flow near harmonic maps. Comm. Pure Appl. Math., 60: 463–499. doi: 10.1002/cpa.20143

Author Information

  1. 1

    Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

  2. 2

    Department of Mathematics and Institute of Basic Science, Sungkyunkwan University, Suwon 440-746, South Korea

Publication History

  1. Issue published online: 24 JAN 2007
  2. Article first published online: 7 JUN 2006
  3. Manuscript Received: APR 2005

Funded by

  • Natural Sciences and Engineering Research Council of Canada
  • Pacific Institute for the Mathematical Sciences Postdoctoral Fellowship

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Abstract

For the Schrödinger flow from ℝ2 × 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.

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