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On Schrödinger maps

From: American Journal of Mathematics
Volume 130, Number 4, August 2008
pp. 1033-1065 | 10.1353/ajm.0.0014

Abstract

Abstract:

We study the local well-posedness theory for the Schr\"odinger Maps equation. We work in $n+1$ dimensions, for $n \geq 2$, and prove a local well-posedness for small initial data in $H^{\frac{n}{2}+ \varepsilon}$.



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