Global existence and uniqueness of Schrödinger maps in dimensions d ≥ 4

I. Bejenaru, A. D. Ionescu, C. E. Kenig

Research output: Contribution to journalArticle

29 Scopus citations

Abstract

In dimensions d ≥ 4, we prove that the Schrödinger map initial-value problem{(∂t s = s × Δ s on Rd × R ;; s (0) = s0) admits a unique solution s : Rd × R → S2 {right arrow, hooked} R3, s ∈ C (R : HQ), provided that s0 ∈ HQ and {norm of matrix} s0 - Q {norm of matrix}over(H, ̇)d / 2 ≪ 1, where Q ∈ S2.

Original languageEnglish (US)
Pages (from-to)263-291
Number of pages29
JournalAdvances in Mathematics
Volume215
Issue number1
DOIs
StatePublished - Oct 20 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • A priori estimates
  • Modified Schrödinger maps
  • Orthonormal frames
  • Schrödinger maps

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