Vol. 2, No. 2, 2009

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

Igor Rodnianski, Yanir A. Rubinstein and Gigliola Staffilani

Vol. 2 (2009), No. 2, 187–209

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.

Schrödinger flow, periodic NLS, cubic NLS, Strichartz estimates, Kähler manifolds
Mathematical Subject Classification 2000
Primary: 35Q55
Secondary: 53C44, 35B10, 32Q15, 42B35, 15A23
Received: 13 November 2008
Revised: 25 February 2009
Accepted: 4 May 2009
Published: 1 May 2009
Igor Rodnianski
Department of Mathematics
Princeton University
Fine Hall
Princeton, NJ 08544
United States
Yanir A. Rubinstein
Department of Mathematics
Johns Hopkins University
3400 N Charles St.
Baltimore, MD 21218
United States
Gigliola Staffilani
Department of Mathematics
Massachusetts Institue of Technology
77 Massachusetts Avenue, 2-246
Cambridge, MA 02139
United States