The Cauchy problem for Schrödinger flows into Kähler manifolds

Pages: 389 - 439, Volume 27, Issue 2, June 2010

doi:10.3934/dcds.2010.27.389       Abstract        Full Text (487.6K)       Related Articles

Carlos Kenig - University of Chicago, United States (email)
Tobias Lamm - University of British Columbia, Canada (email)
Daniel Pollack - University of Washington, United States (email)
Gigliola Staffilani - Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, United States (email)
Tatiana Toro - Department of Mathematics, University of Washington, Seattle, Washington 98195–4350, United States (email)

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

Keywords:  Schrödinger flows, Energy Estimates, Cauchy Problem.
Mathematics Subject Classification:  Primary: 35Q55; Secondary: 58J35.

Received: October 2009;      Revised: February 2010;      Published: February 2010.