Analysis & PDE

  • Anal. PDE
  • Volume 2, Number 2 (2009), 187-209.

On the global well-posedness of the one-dimensional Schrödinger map flow

Igor Rodnianski, Yanir Rubinstein, and Gigliola Staffilani

Full-text: Open access

Abstract

We establish the global well-posedness of the initial value problem for the Schrödinger map flow for maps from the real line into Kähler manifolds and for maps from the circle into Riemann surfaces. This partially resolves a conjecture of W.-Y. Ding.

Article information

Source
Anal. PDE, Volume 2, Number 2 (2009), 187-209.

Dates
Received: 13 November 2008
Revised: 25 February 2009
Accepted: 4 May 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513798016

Digital Object Identifier
doi:10.2140/apde.2009.2.187

Mathematical Reviews number (MathSciNet)
MR2547134

Zentralblatt MATH identifier
1191.35258

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 35B10: Periodic solutions 32Q15: Kähler manifolds 42B35: Function spaces arising in harmonic analysis 15A23: Factorization of matrices

Keywords
Schrödinger flow periodic NLS cubic NLS Strichartz estimates Kähler manifolds

Citation

Rodnianski, Igor; Rubinstein, Yanir; Staffilani, Gigliola. On the global well-posedness of the one-dimensional Schrödinger map flow. Anal. PDE 2 (2009), no. 2, 187--209. doi:10.2140/apde.2009.2.187. https://projecteuclid.org/euclid.apde/1513798016


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