On Schr\"odinger Maps

TL;DR

This paper establishes local well-posedness for the Schr"odinger Maps equation in higher dimensions with small initial data in a specific Sobolev space, advancing understanding of its mathematical properties.

Contribution

It proves local well-posedness for Schr"odinger Maps in dimensions n+1 with small initial data in H^{n/2+ε}, extending previous results to higher dimensions.

Findings

Proves local well-posedness in dimensions n+1 for n ≥ 2.

Demonstrates well-posedness for small initial data in H^{n/2+ε}.

Advances mathematical understanding of Schr"odinger Maps.

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 $H^{\frac{n}{2}+\e}$.