Well-posedness and blowup for the dispersion-managed nonlinear Schrödinger equation

We consider the nonlinear Schrödinger equation with periodic dispersion management. We first establish global-in-time Strichartz estimates for the underlying linear equation with suitable dispersion maps. As an application, we establish a small-data scattering result for the 3 d 3d cubic equation. Finally, we use a virial argument to demonstrate the existence of blowup solutions for the 3 d 3d cubic equation with piecewise constant dispersion map.