Schrödinger flow near harmonic maps
Article first published online: 7 JUN 2006
Copyright © 2006 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Volume 60, Issue 4, pages 463–499, April 2007
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
- Issue published online: 24 JAN 2007
- Article first published online: 7 JUN 2006
- Manuscript Received: APR 2005
- Natural Sciences and Engineering Research Council of Canada
- Pacific Institute for the Mathematical Sciences Postdoctoral Fellowship
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.