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

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.$