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

Wang, Baoxiang
Wang, Yuzhao
Description
In this paper we study the Cauchy problem for the elliptic and non-elliptic derivative nonlinear Schr\"odinger equations in higher spatial dimensions ($n\geq 2$) and some global well-posedness results with small initial data in critical Besov spaces $B^s_{2,1}$ are obtained. As by-products, the scattering results with small initial data are also obtained.
Comment: 26 pages
Keywords
Mathematics - Analysis of PDEs, 35Q55, 42B37