Global well-posedness and scattering for Derivative Schr\"{o}dinger equation

In this paper we study the Cauchy problem for the elliptic and non-elliptic derivative nonlinear Schr"odinger equations in higher spatial dimensions ($n\ge 2$) and some global well-posedness results with small initial data in critical Besov spaces $B_{2,1}^s$ are obtained. As by-products, the scattering results with small initial data are also obtained.