Schrödinger flow near harmonic maps

S. Gustafson, K. Kang, T. P. Tsai

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

For the Schrödinger flow from ℝ2 × ℝ+ to the 2-sphere S2, 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.

Original languageEnglish
Pages (from-to)463-499
Number of pages37
JournalCommunications on Pure and Applied Mathematics
Volume60
Issue number4
DOIs
Publication statusPublished - 2007 Apr

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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