On well-posedness of the s-Schr\"odinger maps in the subcritical regime

TL;DR

This paper proves local well-posedness for the s-Schr"odinger map equation in higher dimensions within the subcritical regime, using initial data in a specific Besov space with small norm.

Contribution

It establishes the local well-posedness of the s-Schr"odinger map in the subcritical regime for initial data in Besov spaces, extending previous results to higher dimensions.

Findings

Well-posedness holds for initial data in B^{rac{n+1}{2}}_{2,1} with small norm.

Results apply to dimensions n ≥ 3.

Provides a framework for analyzing s-Schr"odinger maps in the subcritical setting.

Abstract

We study well-posedness of the $s$-Schr\"odinger map equation in dimension $n \geq 3$ in the subcritical regime, more precisely we establish a local well-posedness result when the initial data is $u_{0} \in B^{\sigma}_{2,1}$ with $ \sigma \geq \frac{n+1}{2}$ and $ \Vert u_{0} \Vert_{B^{\sigma}_{2,1}} \ll 1.$