The Cauchy problem for Schrödinger flows into Kähler manifolds

Carlos Kenig; Tobias Lamm; Daniel Pollack; Gigliola Staffilani; Tatiana Toro

doi:10.3934/dcds.2010.27.389

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2010, Volume 27, Issue 2: 389-439. Doi: 10.3934/dcds.2010.27.389

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The Cauchy problem for Schrödinger flows into Kähler manifolds

1.
University of Chicago
2.
University of British Columbia
3.
University of Washington
4.
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307
5.
Department of Mathematics, University of Washington, Seattle, Washington 98195–4350

Received: September 30, 2009

Revised: January 31, 2010

Published: June 2010

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Abstract

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 $s\geq[\frac{n}{2}]+4$.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 58J35.

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