Continuous dependence for NLS in fractional order spaces

Thierry Cazenave, Daoyuan Fang, Zheng Han

We consider the Cauchy problem for the nonlinear Schrödinger equation $i{u}_t+\Delta u+\lambda |u{|}^{\alpha }u=0$ in ${\mathbb{R}}^N$, in the $H^s$-subcritical and critical cases $0<\alpha \le 4/(N-2s)$, where $0<s<N/…