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On the global
well-posedness of the one-dimensional Schrödinger map
flow
Igor Rodnianski, Yanir A. Rubinstein and Gigliola Staffilani |
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Vol. 2 (2009), No. 2, 187–209
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Abstract |
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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. |
Keywords
Schrödinger flow, periodic NLS, cubic NLS, Strichartz
estimates, Kähler manifolds
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Mathematical Subject Classification 2000
Primary: 35Q55
Secondary: 53C44, 35B10, 32Q15, 42B35, 15A23
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Milestones
Received: 13 November 2008
Revised: 25 February 2009
Accepted: 4 May 2009
Published: 1 May 2009
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Authors |
| Igor Rodnianski | |
| Department of Mathematics Princeton University Fine Hall Princeton, NJ 08544 United States |
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| Yanir A. Rubinstein | |
| Department of Mathematics Johns Hopkins University 3400 N Charles St. Baltimore, MD 21218 United States |
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| Gigliola Staffilani | |
| Department of Mathematics Massachusetts Institue of Technology 77 Massachusetts Avenue, 2-246 Cambridge, MA 02139 United States |
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| http://www-math.mit.edu/~gigliola/ | |
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