Local existence, global existence, and scattering for the nonlinear Schrödinger equation

In this paper, we construct for every $α>0$ and $λ\in {\mathbb C}$ a space of initial values for which there exists a local solution of the nonlinear Schrödinger equation \begin{equation*} \begin{cases} iu_t + Δu + λ|u|^αu= 0 \\ u(0,x) = u_0 \end{cases} \end{equation*} on ${\mathbb R}^N$. Moreover, we construct for every $α>\frac {2} {N}$ a class of (arbitrarily large) initial values for which there exists a global solution that scatters as $t\to \infty$.

No reviews yet.

No comments yet.