Analysis & PDE
- Anal. PDE
- Volume 2, Number 2 (2009), 187-209.
On the global well-posedness of the one-dimensional Schrödinger map flow
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.
Anal. PDE, Volume 2, Number 2 (2009), 187-209.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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