Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger Equation in $H^s$

Wei Dai, Weihua Yang, Daomin Cao

We consider the Cauchy problem for the nonlinear Schrödinger equation $i{\partial }_{t}u+\Delta u={\lambda }_{0}u+{\lambda }_1|u{|}^{\alpha }u$ in ${\mathbb{R}}^N$, where ${\lambda }_0,{\lambda }_1\in \mathbb{C}$, in $H^s$ subcr…