Schrödinger maps

Nai Heng Chang, Jalal Shatah, Karen Uhlenbeck

Research output: Contribution to journalArticlepeer-review

Abstract

We study the well-posedness of the Cauchy problem for Schrödinger maps from ℝm × ℝ into a compact Riemann surface N. The idea is to find an appropriate frame for u-1TN so that the derivatives will satisfy a certain class of nonlinear Schrödinger equations; then the Strichartz estimates can be applied to obtain a priori estimates. We treat the problem with finite energy data for m = 1 and with small energy data for m = 2 under an assumption of radial or script S sign1 symmetry on N.

Original languageEnglish (US)
Pages (from-to)590-602
Number of pages13
JournalCommunications on Pure and Applied Mathematics
Volume53
Issue number5
DOIs
StatePublished - May 2000

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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