Continuous Dependence of Cauchy Problem For Nonlinear Schr\"{o}dinger Equation in $H^s$

We consider the Cauchy problem for the nonlinear Schr"{o}dinger 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$H^s$subcriticalandcriticalcase:$0<\alpha\leq\frac{4}{N-2s}$when$1<s<\frac{N}{2}$and$0<\alpha<+\infty$when$s\geq\frac{N}{2}$. We show that the solution depends continuously on the initial value in the standard sense in $H^s({\mathbb{R}}^N)$ if $\alpha$ satisfies certain assumptions.