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May  2010, 27(2): 389-439. doi: 10.3934/dcds.2010.27.389

The Cauchy problem for Schrödinger flows into Kähler manifolds

Carlos Kenig 1, , Tobias Lamm 2, , Daniel Pollack 3, , Gigliola Staffilani 4, and  Tatiana Toro 5,

1. 

University of Chicago, United States
2. 

University of British Columbia, Canada
3. 

University of Washington, United States
4. 

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307
5. 

Department of Mathematics, University of Washington, Seattle, Washington 98195–4350

Received  October 2009 Revised  February 2010 Published  February 2010

We prove local well-posedness of the Schrödinger flow from $\RR^n$ into a compact Kähler manifold $N$ with initial data in $H^{s+1}(\RR^n,N)$ for $s\geq[\frac{n}{2}]+4$.
Keywords: Cauchy Problem., Schrödinger flows, Energy Estimates.
Mathematics Subject Classification: Primary: 35Q55; Secondary: 58J3.
Citation: Carlos Kenig, Tobias Lamm, Daniel Pollack, Gigliola Staffilani, Tatiana Toro. The Cauchy problem for Schrödinger flows into Kähler manifolds. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 389-439. doi: 10.3934/dcds.2010.27.389
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