Scattering from a finite Strichartz norm
= Scattering from a finite Strichartz norm
If a global cubic Schrödinger solution has finite $L^4_{t,x}$ norm on a time ray, the dual Strichartz estimate makes its interaction representation Cauchy in $L^2$. It therefore converges to scattering data $u_\infty$, and $u(t)-e^{it\Delta}u_\infty\to0$ in $L^2$.