Local existence, global existence, and scattering for the nonlinear Schrödinger equation
Local existence, global existence, and scattering for the nonlinear Schrödinger equation
In this paper, we construct for every $\alpha >0$ and $\lambda \in {\mathbb C}$ a space of initial values for which there exists a local solution of the nonlinear Schr\"odinger equation \begin{equation*} \begin{cases} iu_t + \Delta u + \lambda |u|^\alpha u= 0 \\ u(0,x) = u_0 \end{cases} \end{equation*} on ${\mathbb …