On well-posedness of the s-Schrödinger maps in the subcritical regime

Abstract: We study well-posedness of the $s$-Schrödinger 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 $u_{0} \in B^σ_{2,1}$ with $ σ\geq \frac{n+1}{2}$ and $ \Vert u_{0} \Vert_{B^σ_{2,1}} \ll 1.$