A note on minimal mass blow up for inhomogeneous NLS

We revisit the work of \cite{raphael2011existence} on the minimal mass blow up solution for $i{u}_t+\mathrm{\Delta }u=-k(x)\mathrm{\mid }u{\mathrm{\mid }}^{2}u$, and extend the construction of such a solution to the $k\in C^2$ case.