# American Institute of Mathematical Sciences

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

## The Cauchy problem for Schrödinger flows into Kähler manifolds

 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 $s\geq[\frac{n}{2}]+4$.
Citation: Carlos Kenig, Tobias Lamm, Daniel Pollack, Gigliola Staffilani, Tatiana Toro. The Cauchy problem for Schrödinger flows into Kähler manifolds. Discrete & Continuous Dynamical Systems, 2010, 27 (2) : 389-439. doi: 10.3934/dcds.2010.27.389
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