Non‐global solutions for the inhomogeneous nonlinear Schrödinger equation without gauge invariance

This work investigates the non‐global existence of solutions for the inhomogeneous nonlinear Schrödinger problem without gauge invariance. Indeed, initially, we establish the non‐global existence of certain mass‐subcritical solutions. Subsequently, we demonstrate the non‐global existence of energy‐subcritical solutions characterized by small initial data. These results are are acknowledged to be unsuccessful for the classical gauge invariant inhomogeneous nonlinear Schrödinger equation (INLS).