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

We study well-posedness of the $s$-Schrödinger map equation in dimension $n\ge 3$ in the subcritical regime, more precisely we establish a local well-posedness result when the initial data is $u_0\in B_{2,1}^{\sigma }$ with $\sigma \ge \frac{n+1}{2}$ and $\mathrm{\parallel }{u}_0{\mathrm{\parallel }}_{B_{2,1}^{\sigma }}\ll 1.$