Non-global solutions to the fractional INLS without gauge invariance

This work investigates the non-global existence of solutions to the inhomogeneous nonlinear fractional Schrödinger problem without gauge invariance. Indeed, we prove the non-global existence of both mass-sub-critical and energy-sub-critical solutions for small datum. This makes an essential difference with the inhomogeneous nonlinear fractional Schrödinger problem with gauge invariance.